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SCIENCE 



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DIVISION 




Library of Congress 




Return To 

sowf m jisf'jviT^Qgy 

f-ibrary of Congress 




t 







SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 



This ck)cument contains information affecting the national defense of the United 
States within the meaning of the Espionage Act, 50 U.S.C., 31 and 32, as 
amended. Its transmission or the revelation of its contents in any manner to 
an unauthorized person is prohibited by law. 

This volume is classified RESTRICTED in accordance with security regula¬ 
tions of the War and Navy Departments because certain chapters contain 
material which was RESTRICTED at the date of printing. Other chapters 
may have had a lower classification or none. The reader is advised to consult 
the War and Navy agencies listed on the reverse of this page for the current 


classification of any material. 




Manuscript and illustrations for this volume were prepared for 
publication by the Summary Reports Group of the Columbia 
University Division of War Research under contract OEMsr-1131 
with the Office of Scientific Research and Development. This vol¬ 
ume was printed and bound by the Columbia University Press. 

Distribution of the Summary Technical Report of NDRC has been 
made by the War and Navy Departments. Inquiries concerning the 
availability and distribution of the Summary Technical Report 
volumes and microfilmed and other reference material should be 
addressed to the War Department Library, Room lA-522, The 
Pentagon, Washington 25, D. C., or to the Office of Naval Re¬ 
search, Navy Department, Attention: Reports and Documents 
Section, Washington 25, D. C. 


Copy No. 

5 


This volume, like the seventy others of the Summary Technical 
Report of NDRC, has been written, edited, and printed under 
great pressure. Inevitably there are errors which have slipped past 
Division readers and proofreaders. There may be errors of fact not 
known at time of printing. The author has not been able to follow 
thi’ough his writing to the final page proof. 

Please report errors to: 

JOINT RESEARCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATa) 

W^ASHINGTON 25, D. C. 

A master errata sheet wall be compiled from these reports and sent 
to recipients of the volume. Your help wall make this book more 



SUMMAKY TECII.MCAL REPORT OF DIVISION 4, NDRC 


VOLUME 2 


BOMB, ROCKET, AND 
TORPEDO TOSSING 


Return To 

SCIENCE AND TECHNOLOGY DIVISION 

>=.. 'N IJbrary of Congress^ 


OFFJCK OF SCIENTIFIC RESEAUCll AND DEVELOPMENT 
VANNEVAK BUSH, DIRECTOR 

N A T I O N A L D E F E N S E R E S E A R CII C O M MIT T E E 
JAMES B. CONANT, CITAIRAIAN 

DIVISION 4 

ALEXANDER ELLETT, CHIEF 




OMS S2C 





WASIITXGTOX, 1). ( ., 


194() 


WAR mmum 

V LIPRARY 

WASHiNGTOi4. D. C, 




NATIONAL DEFENSE RESEARCH COMMITTEE 


» -JAN12 


James B. Conant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams Army Representative ‘ 

Frank B. Jewett Navy Representative * 

Karl T. Compton Commissioner of Patents ^ 

Irvin Stewart, Executive Secretary 


' Army representatives in order of service: 

Maj. Gen. G. V. Strong Col. L. A. Den.son 
Alaj. Gen. R. C. Moore Col. P. R. Faymonville 
Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier 
Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine 
Col. E. A. Routlieau 


2 Navy representatives in order of service: 

Rear Adm. II. G. Bowen Rear Adm. J. A. Furer 

Cajit. Lybrand P. Smith Rear Adm. A. 11. Van Keureii 

Commodore H. A. Schade 
® Commissioners of Patents in order of service: 
Conway P. Coe Casper W. Ooms 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities of 
warfare, together with contract facilities for carrying out 
these projects and programs, and (2) to administer the 
technical and scientific work of the contracts. ISIore specifi¬ 
cally, NDRC functioned by initiating research jwojects on 
requests from the Army or the Navy, or on requests from an 
allied government transmitted through the Liaison Office 
of OSRD, or on its own considered initiative as a result of 
the experience of its members. Proposals prepared by the 
Division, Panel, or Committee for research contracts for 
performance of the work involved in such projects were 
first reviewed by NDRC, and if approved, recommended to 
the Director of OSRD. Upon approval of a proposal by the 
Director, a contract permitting maximum flexibility of 
scientific effort was arranged. The business aspects of the 
contract, including such matters as materials, clearances, 
vouchers, patents, priorities, legal matters, and administra¬ 
tion of patent matters were handled by the Executive 
Secretary of OSRD. 


In a reorganization in the fall of 1942, twent^’-three 
administrative divisions, panels, or committees were cre¬ 
ated, each with a chief selected on the basis of his outstaiid- 
ing work in the particular field. Tlie NDRC members then 
became a reviewing and advisory grouj) to the Director of 
OSRD. The final organization was as follows; 

Division 1 — Ballistic Re.search 

Divi.sion 2 — Effects of Imjiact and Exiilosion 

Division .‘I — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Exjilosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 11 —Chemical Engineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 


Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These Mere: 

Division A — Armor and Ordnance 
Division B — Bombs, Fuels, Ga.ses,& Chemical Problems 
Dixdsion C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
Division E — Patents and Inventions 


iv 







201? 


490930 


Division 15 — Radio Coordination 
Division 16 — Optics and Camouflaj 
Division 17 — Physics 
Division 18 — War Metallurgy 
Division 19 — ^Miscellaneous 
.Applied Mathematics Panel 
Applied Psychology Panel 
Committee on Propagation 
Tropical Deterioration Administrative C(^ 









NDRC FOREWORD 


As EVENTS of the years ])re(*e(ling 1940 revealed 
more and more clearly the seriousness of the 
world situation, many scientists in this country came 
to realize the need of organizing scientific research for 
service in a national emergency. Recommendations 
which they made to the White House were given 
carefnl and sympathetic attention, and as a result the 
Xational Defense Research C'ommittee [XDRC] was 
formed by Executive Ordei’ of the President in the 
.summer of 1940. The members of NDRC, appointed 
by the President, were instructed to supplement the 
work of the Army and the Navy in the development 
of the instrumentalities of war. A year latei', upon 
the establishment of the Office of Scientific Research 
and Development [OSRD], XDRC became one of its 
units. 

The Summary Technical Report of X’DRC is a 
conscientious effort on the part of X"DRC to sum¬ 
marize and evaluate its w'ork and to present it in a 
useful and permanent form. It comprises some 
seventy volumes broken into groups corresponding 
to the X"DRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The report of each group contains a 
summary of the report, stating the problems pre¬ 
sented and the philosophy of attacking them, and 
summarizing the results of the research, develo})- 
ment, and training activities undertaken. Some 
volumes may be “state of the art” treatises covering 
subjects to which various research groups have 
contributed information. Others may contain de¬ 
scriptions of de\dces developed in the laboratories. 
A master index of all these divisional, panel, and 
committee reports which together constitute the 
Summary Technical Report of X^DRC is contained 
in a separate volume, which also includes the index 
of a microfilm record of pertinent technical laboratory 
reports and reference material. 

Some of the X^DRC-sponsored researches which 
had been declassified by the end of 1945 were of 
sufficient popular interest that it was found desirable 
to report them in the form of monographs, such as 
the series on radar by Division 14 and the monograph 
on sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not 
duplicated in the Summary Technical Report of 
XDRC, the monographs are an important part of 
the story of these aspects of XDRC research. 


In contrast to the information on radar, which is of 
w'idespi-ead interest and much of which is releasefl 
to the public, the research on subsurface w’arfare is 
lai-gely classifiefl and is of general interest to a more 
resti'icted group. As a consequence, the report of 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over tw'enty volumes. 
The extent of the work of a Division cannot therefoi'e 
be judged solely by the number of volumes devoted 
to it in the Summary Technical Report of X’DRC; 
account must be taken of the monographs and avail- 
aide reports iniblished elsew'here. 

The program of Division 4 in tlie field of electronic 
ordnance provides an excellent example of the 
manner in which reseai'ch and development wmrk 1)_\" 
a ci\41ian technical group can complement and 
supjjlement w'ork done by the Armed Services. The 
greatest responsibility of Di\ ision 4, under the lead¬ 
ership of Alexander Ellett, was to undertake the 
development of proximity fuzes for nonrotating or 
fin-stabilized missiles, such as bombs, rockets, and 
mortar shells. 

Early work on fuzes of various types indicated 
that those operating through the use of electro¬ 
magnetic waves offered the most promise; the 
eventual device depended on the doppler effect, 
combining the transmitted and received signals to 
create a low' frequency ))eat w’hich triggered an 
electronic swdtch. During the last phases of the war 
against Japan, approximately one-third of all tlie 
bomb fuzes used by carrier-based aircraft wnre 
proximity fuzes. For improving the accuracy of 
bombing operations the Division developed the toss 
bombing technique, by w'hich the effect of gravity 
on the flight path of the missile is estimated and 
allowed for. The success of this technique is tlemon- 
strated by its combat use, wJien a circle of probable 
error as low' as 150 feet w'as obtained. 

The Summary Technical Report of Division 4 
W'as prepared under the direction of the Division 
Chief and has been authorized by him for publication. 
We w'ish to pay tribute to the enterprise and energy 
of the members of the Division, w'ho w'orked so 
devotedly for its success. 

Vannevar Bush, Director 
Office of Scientific Research and De^opynent 

J. B. CoNANT, Chairman 
National Defense Research Committe^^ 






FOREWORD 


T he attempt to get proximity fuzed projectiles 
into air-to-air combat was resi^onsible for the 
develoi)ment of toss boml)ing. This technique arose 
out of conversations between Colonel H. S. Alorton 
(jf the Army Ordnance Department and the Chief 
of Division 4 in January 1943. That these discus¬ 
sions ultimately led to the evolution of a successful 
teclmicpie is due very largely to Colonel INIorton’s 
enthusiastic and effective sui)port during the early 
stages of the development. Through the cooperation 
of the Ordnance Department, planes and testing 
facilities were made available at Aberdeen at a time 
when toss bombing was merely an idea. Without 
the assistance of the Ordnance Department through¬ 
out the early and often disappointing trials with 
breadboard equipment, the technicpie could not 
have been developed to a useful form. 

When the development had ]n-ogressed to such a 
state that the feasibility of the technique was fairly 


evident, the Army Air Forces and later the Navy 
offered cooperation. Testing in connection with pilot 
production and production models was carried out 
very largely under Navy auspices at Patuxent and 
Inyokern. Much credit is due to personnel of both 
these stations for enthusiastic and effective coop¬ 
eration. 

Development of eciuipment for toss bombing was 
carried on in the Division’s Central Laboratory at 
the National Bureau of Standards and at the State 
L'niversity of Iowa. The personnel primarily 
responsible were AVilliam B. McLean, J. Babinow, 
W. L. Whitson, and W. S. Ilinman, Jr., of the Na¬ 
tional Bureau of Standards and James A. Jacobs and 
1. H. Swift of the University of Iowa. 

Alexander Ellett 
Chief, Division 4 



vii 











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PREFACE 


T his volume of the Division 4 Summary Technical 
Report covers work done on the development 
and evaluation of etiuipment for tossing homl)s, 
rockets, and torpedoes. 

The toss teclmiipie was conceived and initiated liy 
Colonel Harold S. Morton, of the Army Oi’dnance 
Department, and liy Dr. Alexander Ellett, C’hief of 
Division 4. The principle of the toss techniiiue is 
explained in the introduction to the volume. Chapter 
1. The introduction also includes a lirief summary of 
the achievements of the program. 

A simplihed theory of the toss techniciue is given 
in Chapter 2, including the principle of instrumenta¬ 
tion. A description of the eciuijiment designed and 
produced is given in Chapter 3, “Instrumentation.” 

Considerable space is devoted to describing the 
early experimental models, which are now obsolete. 
These descriptions are included primarily because 
almost all of the evaluation studies which were made 
on the equiinnent were carried out with experimental 
models. Production models, which incorporated a 
number of desirable improvements, were not a’vmil- 
able until just before the end of the war, at which 
time Division 4 transferred sponsorship of the 
project to the Navy. 

The problems of installation and maintenance of 
the equipment in aircraft under Seindce conditions 
are presented in Chapter 4. 

A summary of the evaluation tests on boml), 
rocket, and torpedo tossing is given in Chapter 5. 

The theoretical formulation of the toss techni([ue 
is presented in some detail in C'hapters 6 and 7, 
supplementing Chapter 2. Inclusion of this material 
is considered important in providing a basis for 
future work. 

The newest ideas for tossing equipment, some of 
which have not reached the stage of development 
where they could be evaluated bj" field tests, are 
included in Chapter 8. 


This V(dume is based to a very apprecialrle extent 
on a comprehensi^'e summary prepared jointly by 
members of Division 4’s central laboratories, the 
Ordnance Development Division at the Xational 
Hureau of Standards, and of the State University 
of Iowa under the editorship of A. C. Iloyem, 
foi'merly of the latter institution and now at the 
Xaval Ordnance Test Station, Inyokern, California, 
and of Francis R. Silsbee, of the X^ational Bureau of 
Standards. The material from that summary has 
been apprecialily revised and rearranged for the 
juirposes of this volume. In this process, invaluable 
assistance was rendered by Emma U. Rotor, of the 
Xational Bureau of Standards, and William B. 
IMcLean, formerly of the X'ational Bureau of Stand¬ 
ards and now at the Xaval Ordnance Test Station, 
Inyokern, California. The authors of the separate 
chapters are named in the table of contents and as 
footnotes to the chapter and section headings. 
Where authorship is not specifically indicated, the 
material was prepared jointly by one or more of the 
aforementioned and the editor. 

Art work in the volume, unless credit is otherwise 
indicated, was prepared by Theodore C. Hellmers, 
13hotographer for Division 4’s central laboratories, 
and E. W. Hunt and his staff of draftsmen at the 
Xational Bureau of Stamlards. The Bibliography 
was compiled and checked by Mrs. Rotor and 
Catherine Pike. 

\Try appreciable credit for this volume is due 
Mrs. Rotor not onh' for the contributions mentioned 
above but also for her diligent supervision of the 
review and assembly of the final manuscript. In the 
latter work she was given able and generous assist¬ 
ance by S. H. Lackenbi’uch, R. L. Eichberg, and 
Betty Hallman. 

A. V. Astin 
Editor 



ix 




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CONTENTS 


CHAPTER page 

1 Introduction. 1 

2 Theory of the Toss IMethod by L. E. Ward, I. H. Swift 

and Albert London . 6 

3 Instrumentation by V. W. Cohen and F. M. Defandorff . 29 

4 Installation, Operation, and Maintenance by P. V. Johnson 49 

5 Evaluation of the Toss Technique by Emma U. Rotor 

and A. G. Hoyem .62 

6 Mathematical Analysis of Bomb Tossing by L. E. Ward 

and Albert London .94 

7 Mathematical Theory of Rocket Tossing by M. E. Rolfs, 

L. E. Ward, P. G. Hubbard, and /. H. Swift . . 139 

8 Development of Improved Tossing Equipment by 
William B. McLean, Albert London, L. E. Ward, and 

S. H. Lachenbruch .162 

Bibliography.183 

OSRD Appointees.194 

Contracts.195 

Service Projects.196 

Index.197 






Frontispiece 


Strike photograph of tlie hrst c-ombat mis.sioii using the toss-bomb teeliiiique. The target was a stores (le{)ot in (.ermany: 
the aiming point was the center of the (luadrangle formed t)y the four rectangular buildings within the circle. Of twelve 
.'lOO-pound bombs dropped, six struck within 12.‘r feet of the aiming i)oint and the maximum disj)lacement was 310 feet. 
(.\rmy .\ir Force photograph.) 





Chapter 1 

INTRODUCTION 


' • THE DIVE-TOSS TECHNIQUE 

T oss BOMBixo provides a method of improving the 
accuracy of homldng operations. The method 
can be used with bombs, rockets, and torpedoes, and 
although applicable primarily to dive attacks, it is 
also effective in level, plane-to-plane attacks. In 
fact, the method can be employed wherever a colli¬ 
sion course with the target can be flown for a short 
pei-iod prior to release of the missile. The object 
of the toss technique is to estimate and allow for the 
effect of gra^•ity on the flight path of the missile. The 
latter is accomplished by releasing the missile from 
the aircraft with sufficient upward velocity above a 
line of sight to compensate for the gravity drop of 
the missile during its flight to the target. The release 
conditions are determined by an instrument which 
measures the time integral of the transverse accelera¬ 
tion of the aircraft during a pull-out above the line 
of sight and then releases the missile when this 
integral has reached the appropriate value as required 
l)y the time-of-flight of the missile. The time-of- 
flight is computed by the instrument prior to pull¬ 
out, while the aircraft is flying a collision course 
toward the tai-get. 

A typical toss liombing attack is illustrated in 
Figure 1. The airplane enters a dive 2,000 to 5,000 
feet above the point at which the projectile will be 
released and attains speed as rapidly as feasible 
during this dive. When the speed has reached a 
value sufficiently high for operation, and with the 
sight properl}'" oriented on the target, the normal 
bomb release switch is closed by the pilot. Two or 
three seconds after the beginning of the timing run, 
a light near the sight comes on, indicating that the 
pilot may commence pulling out of the dive. When 
the angle through which the airplane has pulled up 
reaches the proper size, as determined automatically 
by the instrument, the release of the missile occurs. 
At this instant, the signal light goes out, indicating 
to the pilot that release has occurred and that 
thereafter he can employ am^ evasive action he 
desires. 

If, after the timing run has l)egun, the pilot decides 
not to complete the manein^er, the action of the 
instrument can be stopped by merely opening the 


bomb release switch. This restores tlie electrical 
circuits to a standby condition. The ecpiipment 
can be made operative again, even in the same dive, 
remaining altitude and other conditions pei'initting, 
by closing again the bomb release switch. 

The development of the toss bombing instrument 
was originally undertaken as a means of attacking 
bomber foi-mations by using fighter airplanes cai’ry- 
ing bombs. It uas initially planned to use a head-on 
approach with high closing speeds and relatively 



Figuee 1. Typical toss bombing maneuver. 


small gravity drops of the bombs after release. The 
development was carried far enough to demonstrate 
that the technique offered excellent advantages as a 
defensive weapon against formations of bombers 
(see Chapter 6; also reference 2G5). However, in 
view of the rapidly increasing scale of the Allied air 
offensive at that time (late summer of 1943), the 
weapon was considered potentially more dangerous 
to Allied than to enemy operations. Work on the 


1 






2 


INTRODUCTION 


air-to-air portion of the project was therefore cur¬ 
tailed, and further development was directed toward 
applying the toss techniciue to dive bombing. 

‘ 2 COMPARISON WITH ORDINARY 
DIVE BOMBING 

The difference between the toss bombing technique 
and ordinary (depressed sight) dive bombing is 
shown schematically in Figure 2. In a dive bombing- 
attack (Figure 2A), the airplane is flown in a line AB 
passing over the target, and the bomb is released 


as determined by the automatic computer, the latter 
causes the release of the bomb. The same method is 
used in torpedo and rocket tossing. 

With the use of the toss technique, much less skill 
is reciuired of the pilot. No visibility below the nose 
of the plane is needed, the range at which a given 
accuracy can l>e attained is much greater, the time 
during which the airplane flies a predetermined 
course is very short (usually about three seconds), 
and the pull-up precerling i-elease constitutes an 
effective preliminary for evasive maneuvers should 
they be necessary. 




Figure 2. Comparison between ordinary dive bombing and toss bombing: (.\) normal dive bombing maneuver; (B) toss 
bombing maneuver. 


manually by the pilot at a point A, which, in his 
judgment, is so related to the speed, dive angle, and 
range, that the gravity drop will carry it down to 
the target. In a toss bombing attack (Figure 2B), 
the plane first dives directly at the target to give 
the automatic computer the necessary data. It then 
pulls out of the dive with the bank indicator centered, 
and when the angle BAT attains the necessary size. 


The tossing techniciue is particularly useful in the 
case of low-velocity, fin-stabilized projectiles, such 
as bombs and the 11.75-in. aircraft rockets, since it 
removes the restriction on range which, in the case 
of the depressed sight technique, is imposed liy 
limited visibility over the nose of the airplane. In 
Figure 3 are graphs which show' the range restrictions 
imposed by various visibility angles w'hen the de- 















SUMMARY OF PERFORMANCE 


3 


pressed sight technique is used in launching bombs 
from an airplane traveling with a speed of 300 
knots. In the same figure, the dotted curve indicates 
the ranges up to which bombs have been successfully 
released by one of the models of the toss bombing 
instrument. 



Figure 3. Theoretical ranges for given sight depres¬ 
sion angles in normal dive bombing (plane velocity = 

300 knots). Dashed curve indicates ranges up to which 
bombs have been successfully released by toss bombing 
equipment. 

The toss equipment provides for the automatic 
release of missiles in dives between 15 and 60 degrees 
at ranges which are subject to the limits imposed 
by the speed of the airplane. Table 1 shows the 
range of operating conditions recommended in toss 
bombing. 

In the case of rockets, the maximum tossing dis¬ 
tance is not restricted by plane speed, since the rocket 
has an additional velocity of its own. Tossing dis¬ 
tances up to 4,500 yards and dive angles ranging 
from 15 to 60 degrees were used with rockets with 
satisfactory results. 


In the tests conducted with torpedoes and using 
airspeeds up to 300 knots, best results were obtained 
when release altitudes were less than 2,000 feet, and 
dive angles between 15 and 25 degrees. 

Table 1. Recommended release conditions for toss 
bombing. Maximum altitudes * (in feet) for (1) closing 
bomb release switch and (2) initiating pull-up (shown 
in italics) as a function of dive angle and airspeed. 


Angle of 
dive 

250 

True airspeed (knots) 
300 350 

400 

15° 


1,900 

1,390 

2,300 

1,668 

2,700 

2,000 

20° 

1,900 

1,390 

2,700 

2,000 

3,200 

2,400 

3,900 

2,880 

30° 

3,200 

2,400 

4,700 

3,450 

5,600 

4,150 

6,800 

4,980 

40° 

4,700 

3,450 

6,800 

4,980 

8,100 

5,975 

11,000 

8,600 

50° 

G,800 

4,980 

9,500 

7,170 

11,000 

8,600 

11,000 

8,600 

(10° 

11,000 

8,600 

11,000 

8,600 

11,000 

8,600 

11,000 

8,600 


* The minimum operating altitude at which the bomb release 
switch may be closed is 1,700 feet, and the corresponding altitude 
below which pull-up may be initiated is 1,390 feet. 


13 SUMMARY OF PERFORMANCE 

Extensive field tests have been made with the 
tossing equipment, using several t 5 "pes of bombs and 
rockets. In the case of bombs, it has been possible to 
conduct overall tactical evaluation tests as well as 
equipment evaluation tests. In the tactical evalua¬ 
tion tests, errors occurring in the allowance for wind 
are superimposed upon equipment errors. In the 
case of rockets, the results of tests on the accuracy 
of the equipment only are available. Conclusions 
regarding the overall accuracy of the tossing equip¬ 
ment may be drawm from these tests, with due 
allowance made for the effect of wind. 

Figure 4 shows the distribution of the impacts of 
747 bombs dropped during a series of evaluation 
tests in which slant ranges varied from 5,400 to 
9,300 feet. The pilots allowed for wind, using 
aerological data and the wind error indicated by the 
first bomb. In general, five bombs were dropped in 
succession. For all the bombs, the 50 per cent circle 
about the target had a radius on the ground of 
100 feet. If the pattern of impacts is projected onto a 
plane normal to the line of flight, 50 per cent of the 





















4 


INTRODUCTION 





I 




T 





500 — 


400 — 


O 



Figure 4. Impact pattern of 747 bombs dropped in jiilots’ evaluation tests at Naval Air Station, Patuxent River, 
Maiyland, October 1944 to August 1945. Slant ranges used varied from 5,400 to 9,300 feet. Distribution of radial errors 
is given in graphical form in inset. 














































MODELS DEVELOPED 


o 


impacts fall within a circle having a radius of 11.5 
mils. As for the errors in range, 50 per cent of the 
impacts show an error of less than 01 feet on the 
ground, or 5.8 mils normal to the line of dive. The 
corresponding deflection errors are 52 feet on the 
ground and 7.8 mils normal to the line of dive. A 
more detailed analysis of these data is given in 
Chapter 5. 



Figure 5. Impact pattern of 82 high-velocity 5.0-iach 
aircraft rockets launched from F6F-5 airplane at Naval 
Ordnance Test Station, Inyokern, California (plotted 
in plane perpendicular to line of flight and corrected to 
no-wind conditions). Test conditions were as follows; 

Slant range 2,050-2,820 yards (avg 2,470) 

Dive angle 30-40 degrees (avg 35) 

True airspeed 300-400 knots (avg 350) 

Figure 5 shows the impact pattern of 82 high- 
velocity 5.0-in. aircraft rockets launched in pairs from 
dives aimed directly at the target. The pattern has 
been corrected to no-wind conditions and hence 
shows where the rockets tvould have hit if the pilot 
had made proper compensation for wind. Fifty 
per cent of the rockets lie within a circle of 9.6 mils 
radius normal to the line of dive. The dashed lines 
in this figure show the limits within w^hich 50 per 
cent of the rockets are located in range and deflection 
respectively. Fifty per cent deviate from the mean 
point of impact by less than 6.3 mils in range and 
7.4 mils in deflection. A more detailed analysis of 
these data also is given in Chapter 5. 

The toss equipment w^as used on a limited number 
of combat missions, in w'hich it gave a circle of 


probable error [CPE] of 200 feet for all rounds re¬ 
leased. Throwing out several rounds where mis- 
identification of the target was established, the CPE 
drops to 150 feet.-®® Further discussion of the 
operational experience is included in Chapter 5. 

MODELS DEVELOPED 

All the data given in the rocket evaluation tests 
and about half the data in the liomb evaluation tests 
just described w'ere obtained using experimental 
equipment designated as bomb director Mark 1 
Model 0, AN/ASG-IOXN. Modifications were 
made to the e.quipment to enable it to release rockets. 
The other half of the data in the bomb evaluation 
tests was obtained using production equipment for 
the release of bombs, designated as bomb director 
Mark 1 Alodel 1, AN/ASG-10. Production equip¬ 
ment for the release of either bombs or rockets is 
designated as bomb director Mark 1 Model 2, 
AN/ASG-IOA. The first production model was 
Service-tested, just before the end of the w^ar, with 
satisfactory results. A later model, designated as 
bomb director Mark 3, AN/ASG-lOB, had reached 
the experimental stage at the end of the war. The 
first three equipments are described in Chapter 3, 
and the Mark 3 in Chapter 8. 

The ]Mark 1 Model 0 equipment was manufactured 
as rapidly as possible in order to serve as a pilot 
model to work out production difficulties, as w'ell 
as to get equipment into the hands of the Services 
for immediate use. Of this model, 500 sets were 
delivered to the Navy, which, in turn, transmitted 
300 of them to the Army. Half of these 300 were 
sent to the European theater, where some w'ere used 
on thirteen combat missions in P-47 airplanes.®®-®®® 

The Mark 1 Model 1 equipment was developed 
on a contract basis by the JMagnavox Corporation 
during the production of the Model 0 units.®®® 
Delivery under this contract began on March 10, 
1945, and by June 30, about 200 sets had been 
turned over to the Navy. Facilities were set up for 
production at an ultimate rate of one thousand per 
month. This rate w'as not reached due to the con¬ 
clusion of the war. Division 4 withdrew from the 
project during August of 1945, at which time the 
Navy Department took over sponsorship of further 
development and production. 













Chapter 2 

THEORY OF THE TOSS METHOD 


2 * BOMB TOSSING" 

Introduction 

C HAPTER 2 GIVES a Simplified exposition of the 
mathematical theory underlying the toss tech¬ 
nique, together with its application to the tossing of 
bombs, rockets, and torpedoes. The basic equations 
are set up and the results of the mathematical treat¬ 
ment are given. Detailed mathematical developments 
are given as supplementary material in Chapters 6 
and 7. Section 2.1 deals with bomb tossing, and the 
succeeding sections deal with rocket and torpedo 
tossing and with wind correction. 

2.1.2 Basic Toss Bombing Eqviations 

Figure 1 is a diagram representing the toss bomb¬ 
ing maneuver, together with the coordinate axes 
commonly used. The point iV represents the position 



Figure 1. Diagrammatic representation of toss bomb¬ 
ing maneuver. (For explanation of symbols, see text.) 


where the bomb release switch is closed, 0 the point 
where pull-up is begun, and NO the flight path 
before pull-up. The extension OH of NO constitutes 

a Section 2.1 was prepared by Dr. L. E. Ward, of the 
Naval Ordnance Test Station, Inyokern, California, and Dr. 
Albert London, of the National Bureau of Standards. 


a collision course to the target at H, assumed 
stationary. The line NOH is used as the x a.xis; 
the y axis is perpendicular to NOH at 0, slanting 
upward. 

Since the airplane is supposed to reach its approxi¬ 
mate final velocity in the dive before the bomb 
release switch is closed, we assume the velocity of 
the airplane to be constant in the theoretical de¬ 
velopments; this velocity is denoted throughout 
by V. The slant range from 0 to H can then be 
represented by the product VTc, where is the 
closing time or time to target at pull-up. This time 
is one of the physical quantities computed by the 
equipment. The actual time interval measured is 
T 12 , the time required to fly from N to 0. Because 
of the assumed constant velocity of the airplane 
between points N and 0, the time Tg is proportional 
to the time T' 12 . The proportionality constant is 
fixed b}'’ designing the equipment to measure an 
arbitrary fraction of the closing time or time to 
target. In the Mark 1 and Mark 3 bomb directors, 
Tc = 5Ti2. 

A fixed ratio between T '12 and Tg is obtained by 
altitude measurements. If hi and hi are the altitudes 
of the points N and 0, then the ratio of /ii to hi must 
be 6:5 in order that Tg = 5Ti2. Further discussion 
of the altitude measurements will be given in 
Section 2.1.4. 

We assume in this development that the pilot 
begins to pull up at 0. The arc OP in Figure 1 
represents the path of the airplane during the 
pull-up. Since this path is curved, the airplane has 
an acceleration normal to its direction of motion at 
each instant. It has no acceleration in its direction 
of motion since the velocity is assumed to remain 
constant. 

Let yg be the acceleration normal to the path at 
any instant. Here, g is the acceleration of gravity, 
M is a number, and the product y.g is what has been 
called the spatial acceleration. Let r be the radius of 
curvature at any instant. Then r = TYfig. Since 
also T = ds/dd where ds is the differential of arc on 
the pull-up path and d is the angle the tangent to 
this path makes with the x axis, it follows that 

dd =- =^^ds = ^dt. (1) 

r V- V 


6 








BOMB TOSSING 


Consoqiientl}', at any time tluring the pull-up 
period, the angle 6 will be given by the integral 


- r 

Y Jo 


ndt, 


_g_ 

'“rX ' 




In terms of /I, equation (3) can be written 


e, = — M. 


and 

Hence, 

and 


X = V cos 9 


y = V sin 9. 


X = VJ cos 9dt 


( 6 ) 


y = V / s\n 9dt. 
Jo 


By using equation (1) to eliminate dt, those equa¬ 
tions become^ 


( 2 ) 


_ r cos 9 
g Jo y 


d9 


where time is measured from the point 0. 

Let the letter p be used as a subscript to denote the 
instant of release of the bomb, so that Tp is the pull-up 
time, that is, the time to fly from the beginning of 
pull-up to the point where the bomb is released; 
9p is the pull-up angle; et cetera. Then, 


(7) 


y 


(3) 


g Jo y 

By placing t = Tp in these relations, expressions are 
obtained for Xp, yp, Xp, and yp. 

After the bomb has been released, the important 
force acting on it is gravity. Hence, for this phase 
of the motion, the components of velocity and the 
coordinates are 


Let the time average of the number y, taken from 
the beginning of pull-up to the release of the bomb, 
be y; i.e., 

1 [Tp 

M = — / ydt. 

I „ Jo 


X = Xp + g{t — Tp) sin a, 

y = yp - gJ - 7^) cos«, 

X = Xp-i- Xp{t - Tp) + \g(t — Tp)~ sin a, 
y = yp ^ yp(t - Tp) - ^g{t - TpY- cos«. 


( 8 ) 


In order to seciu’e a hit, x must equal VTc when 
y = 0. Let this occur when t = T^, so that, from 
equations (8), 


(4) 


A standard aircraft accelerometer mounted in an 
airplane shows at each instant during pull-up the 
number K of g’s present at that instant and acting 
normal to the direction of motion. If a is the dive 
angle, then approximately 

yg ^ {K - cos a)g. (5) 

This relation is sufficiently accurate to be useful for 
small pull-up angles. It is exact at the beginning of 
pull-up since in the dive, K = cos a and ^ = 0- 
The error in subsequent calculations based on equa¬ 
tion (5) will be considered in more detail in Chapter G. 

If X and y are the coordinates of the bomb at any 
time, t, always measured from the beginning of 
pull-up, then the components of velocity on the 
coordinate axes at any instant during pull-up are 


VTc = ojp+XpiTh - Tp) + ^g(T/, - TpY sin a, 
^ = yp + yp{Th - Tp) - \g{Th - TpYdOQ a. 


(9) 


On replacing Xp, yp, Xp, and?/^ by their values from 
equations (6) and (7), equations (10) are obtained. 


VTc = — 

g 


z! r 

g Jo 


p cos 9 


d9 + V(T;, — Tp) cos 9p 


+ hg^T/i — Tp) siiT a; 


( 10 ) 


0 = 1:! 


"p sin 9 


- d9 -b V(T/, — Tp) sin 9p 

g Jo y 

- \gJTh - Tp)- cos a. 

Equations (10) are the basic ecpiations from which 
the toss bombing computer tletermines the proper 
release time Tp. The procedure in general is to 
eliminate Th from the equations, obtaining an 
expression for Tp in terms of Tc, V, 9, and a. The 
value for Tc is obtained during the timing run, a is 
given by a dive angle indicator, and 9 is determined 
in terms of pidl-up acceleration. V occurs only as a 
minor correction term and the ecpiipment is set for 
an average operating value. When values for these 
parameters are fed into the computer, the release 
time is automatically determined. 


b Certain details concerning the convergence of these im¬ 
proper integrals are slurred over here. 






8 


THEORY OF THE TOSS METHOD 


A first step in solving the ecpiations is to eliminate 
the quantit}" (T* — 1\) between the pair of equa¬ 
tions (10). Solving the second of equations (10) for 
(Tfi — Tp) and substituting the expression thus 
obtained into the first gives 

T,-Tp=—^> 
g cos a 

l^sin smHp + 2 cos a j "" (11) 

and 

gTc _ cos a cos Op + sin a sin Op 
V cos^ a 

l^sin Op + sin2 Op+2 cos a 
-b /'"’^^r/e + tana /(12) 

Jon Jo n 

In equation (11), the positive sign, as written, is the 
only sign which can be associated with the radical, 
since the use of a negative sign would make less 
than Tp. 

Equation (12) can be regarded as fundamental to 
further discussion. While it could be written in a 
slightly more compact form as regards the trigono¬ 
metric functions, the present form is more useful for 
the purpose of the approximations to be made in 
Section 2.1.3. 


2.1.3 Approximate Solution 

for Release Time 

An approximate solution of equation (12) will be 
developed in this section. This solution is called the 
zero order solution,^®^ and it is mechanized by the 
Model 0 bomb tossing equipment. In Section 6.1.2 is 
found a more accurate solution, called the first order 
solution,®^ which is mechanized by the Model 1 
equipment, while in Sections 6.1.3, 6.1.4, and 6.1.5 
is found an exact solution of the equation. 

In obtaining the zero order solution of equation 
(12), the first step is to replace g in the integrals by ji. 
Approximate values for the integrals can then be 
found. The resulting form of the relation is 

gTc _ cos a cos Op 4- sin a sin Op 
V cos- a 

sin Op -f J sin- Op + 2 cos a — 

-f — sin 0p+ tan a. (13) 


Next, the trigonometric functions sin Op and cos Op 
are replaced by Op and I — Op-, respectively, on the 
assumption that i)ull-up angles will be small. The 
resulting equation in Op has the form 


gTc _ i\ - \0p-) cosa~ Opsina 

^- 

y cos- a 


1 


MV.-' 


1 1 

— COS a 

P- J 


— Op ~\ - Op- tan a. (14) 

M 2/z 


This ccjuation is seen to be an equation of degree 3 
in Op. However, since the solution sought is expected 
to be valid only for small pull-up angles, we may 
ignore the term of degree 3 in Op, at least if cos a is 
not too small. This leaves the following quadratic 
equation in Op. 


(l-f2(r)V tan a 4-2( l-|-(r)0p- = 0, (15) 

where 

/I -r V /I (/I -j- COS a) 

a = - • 

COS a 


The corresi)onding equation for Tp, obtained by 
using equation (4), is 

gfT/ tan a + (I + ~ = 0. (16) 

2 V 

The positive solution of equation (16), designated 
'hY TpQ (to indicate the zero order solution for Tp) is 

T - ‘^Tc 

1 po -^ , 

1^1 + (T (1 + ^)2 q_ 2 L±^^^r^tanaJ 

or 

Tc cos a 2 

Tpo = - , —.. . 7- ,(17) 

n -f cos a 4- V)u (^t -f- cos a) 14- Y1 4- 2/8 

where 

1 +2t ggptan^ = g^Min^- P -. 

( 14 - 0 -)- 1 V ju-t-cosa 


Let K designate the time average of K from the 
l)eginning of pull-up until the release of the bomb. 
From equation (5) it follows that K = p cos a, 
so that equation (17) can be expressed in the form 


7’ n = 3 : 


Tc cos a 


where 


K 4 -V/v(/v - cos a) 14 - Vl -b 2/3 


^ _ gTc sin a K — cos a 

^ r R ■ 


, ( 18 ) 






































BOMB TOSSING 


9 


Ill mechanizing equation (18) by means of the 
Model 0 equipment, it was found desirable to rewrite 
it in the form 

7 -==^ -Ao, (19) 

K + V/v2 - K 

where 

I /v + V/v - — K 2 cos a 

ro —^- — - - ^ 

K + V/v (/v - cos a) 1 + Vl + 2/3 ’ 

1 he particular property of the i/'o function which 


makes it useful in this connection is that, although 
it is a function of the three variables K, a, and Tg/V, 
it is chiefly a function of a, showing but little varia¬ 
tion with K and Tg/V over the ranges of values of K 
and I'c/V wdiich occur in bomb tossing. This point 
is discussed in detail in Section G.l. How'ever, 
Figures 2 and 3 show how the dependence of i/'o on 
the major variable, a, is affected by different repre¬ 
sentative values of T^/V and 

Since reduces to unity when o: = 0, and since 



Figvre 2. lAo versus dive angle for different values of Tc/V, K being constant ( = 3). 


K-=5 



Figure 3. lAo versus dive angle for different values of K, Tc/V being constant (= 0.02). 

















10 


THEORY OF THE TOSS METHOD 


\po shows relatively little change when K and Tc/V 
are varied, equation (19) shows that \pQ can be re¬ 
garded as a factor whose purpose is to reduce the 
pull-up time from that for horizontal bombing to the 
correct value for bombing from a dive. 

^ Mechanization of the Basic 
Equation 

On referring to equation (19), it is clear that if the 
physical (juantities K, and a can be measured or 
computed while in the dive and the pull-up and then 
combined according to this equation, the correct 
release time will have been found. Some means 
should also be provided to take care of the effect on 
Tpo of changes in the ratio Tc/V. 


mechanization is shown in Figure 4. A full descrip¬ 
tion of the circuits is given in Chapter 3. 

The altimeter is arranged so as to cause a con¬ 
denser of capacity Ci = 2/if to charge for the period 
Ti 2 or Tc/5, corresponding to the time required for 
the altimeter reading to drop to five-sixths of its 
initial value. Initiation of this charging process 
occurs at “the first altitude point” of the altimeter. 
The charging voltage, Va, applied to this capacitor, is 
obtained from a potentiometer built into the artificial 
horizon. This voltage decrea.ses as the dive angle 
increases as determined by the \^o function. The 
voltage Vi built up across Ci is given by the equation 

(l - (-20) 

where Ri = 2 megohms. 



The instrumentation of the Mark 1, Models 0 and 
1 bomb directors consists of an electronic computer 
which receives the values of Rc, K, and a. from three 
electromechanical components and combines them 
in accordance with equation (19) so as to furnish 
automatically the value of Tpo and Tp\, respectively. 
{Tpi is the first order solution for Tp mechanized in 
the Model 1 equipment.) The value of is obtained 
from a suitably modified altimeter, the value of K 
from an accelerometer, and the value of a from an 
artificial horizon modified so as to measure the dive 
angle. A simplified schematic arrangement of the 


After the completion of this operation, which is 
accomplished during the timing run {N to 0 in 
Figure 1), a second condenser of capacity Co = 2juf is 
charged, starting at the “second altitude point” of 
the altimeter; charging continues during pull-up 
from a voltage I'o applied through a resistor R(K) 
which varies in accordance with the acceleration 
present at each instant during the pidl-up. The 
charge q, acquired by Co at time, t, is the solution 
of the differential equation 

^9 + ^ = Eo, (21) 



























BOMB TOSSING 


11 


where R is to be regarded as a function of t, since K 
varies with t. 

The solution of equation (21), which is zero when 
t = 0, is 

q = Cs!>«[ 1 - /.'■“'■"I . 

Hence, the voltage across C 2 is 

c = ^>o[l - (22) 

The release of the bomb is effected by the firing 
of a thyratron when the voltage across Ci equals that 
across C 2 ; that is, the release of the bomb occurs 
when 

r„(l - Vo(l - . (23) 


The resistor R consists of a stack of 84 resistors, 
each resistor being connected between two suc¬ 
cessive conducting segments which are separated 
by thin mica washers. For K > 1.3, this resistor 
obeys the relation in the Model 0; 

R = -in megohms, 

Jv+VX2 -K 

so that as K increases, R decreases nearly propor¬ 
tionally. Thus, the right-hand member of equation 
(23) becomes 

„^(l (1 _ IOC.) f> (X + VM)i. y 

(24) 



Figure 5. Toss bombing trajectories (theoretical) for perfect release time and for release times in error by =fc 10 per cent. 
(Latter are represented by broken curves on either side of unbroken curve.) Dive angle = 30 degrees; tx = time of arrival 
at target, in seconds, measured from release. 






























12 


THEORY OF THE TOSS METHOD 


The potentiometer caixl in the artificial horizon 
is designed so that 


j _ SRiCi) 

2 _^-Tc/5R,Ci 


= ro'/'o 


’/'O Tc 

2\blUC\ 


2!5/^iCi 



(25) 


For Tc < < 5/?i(h, this is nearly eciuivalent to 
?’a = i’DiAo. Using this value to eliminate i\ in 
equation (24) and remembering that the exponential 
terms are small, gives 

(/v + V A'2 - K) dt. (2()) 

./ 0 


Equation (26) gives the same value for 7p as does 
eciuation (19) since K + V A'2 - A' is the average 
value of the A function. 

The actual potentiometer card in the artificial 


horizon, the so-called i/' card, must be designed to 
give i^erfect agreement with the theoretical value of 
\p for one particulai- design value of K, and Tg/V. 
In the Model 1 bomb director, as explained in detail 
in Chapter 7, the design centers of A = 3 and 
Tc/y = 0.028 have been chosen.The variation 
of the theoretical value of \}/ with A is quite negligible 
(Figure 3). However, \{/ does vary to some extent 
^^ith T/y, since 4^ decreases with increasing 7VF 
(Figure 2). The nonlinear charging characteristic 
of the condensers used in the computing circuit is of 
assistance here, since less })roportionate charge 
accumulates on the condenser with increasing charg¬ 
ing time and hence with increasing Tc or Tc/y at a 
fixed F. As a result of this nonlinear characteristic, 
there is considerable agreement between the instru¬ 
mental 4/ and the theoretical 4^ foi‘ values of 
Tc/y different from 0.028, as shown in Figure 8 
in Chapter (>. 



1000 2000 3000 4000 

HORIZONTAL DISTANCE (FEET) FROM SECOND ALTITUDE POINT 


Fiourk (i. T().s.s l)()mhing trajectories (theoretical) for perfect release time and for release times in error hy ±10 per cent. 

(Latter are rei)resente(l hy broken curves on either side ()f md)roken curve.) Dive angle = 45 degrees; Ij- = time of 
arrival at tai'get, in seconds, measured from relea.se. 






























SECOND ALTITUDE (FEET) 


BOMB TOSSING 


13 



Figure 7. Toss IioinbiiiK trajectories (theoretical) for perfect release time and for release times in error by ± 10 per cent. 
(Latter are represented by broken curves on either side of unbroken curve.) Dive an}?le = 00 degrees ;< 7- = time of arrival 
at target, in seconds, measureil from release. 

















































14 


rilKORY OF THE TOSS METHOD 


2.1.5 Trajectories, Release Conditions, 
and Restrictions 

Figures 5, (), and 7 show computed trajectories for 
dive angles of 30, 45, and GO degrees, respectively, 
other conditions being indicated on the figures and 
in the captions.*^® 

The indicated trajectories are for perfectly esti¬ 
mated release times, 7p. Shown also in the curves 
(in the neighborhood of the target only) are the 
theoretical trajectories for release times in error by 



Figurk 8. C'urves of constant pnll-up times, 1' = .jOO 
feet/second, /v = 3. 

plus and minus 10 per cent. The horizontal range 
errors decrease rapidly with increased angle of dive, 
and for the three cases shown, are approximately 
150, 50, and 25 feet, corresponding to 3.5 per cent, 
2 per cent, and 1.5 per cent of the total horizontal 
range. The curves are extended both above and 
below the theoretical hoiizon so that the variation 
of the error with the altitude of i-elease may be 
estimated. 

For certain evaluations, it is of interest to deter¬ 
mine the range of operating conditions for various 
pull-up times and pull-up angles.^® Figure 8 is a chart 


showing contours of constant pull-up times, i.e., 
each chart represents the spatial coordinates (at the 
start of pull-up) of various maneuvers which result 
in the same value of 7 p. By following, for example^ 
the curve labeled 2.0, the various conditions requir¬ 
ing a pull-up time of 2 seconds are found. The condi¬ 
tions A' = 3 and V = 500 feet/second are assumed. 
In the same way. Figure 9 is a chart showing contour 
curves of constant pull-up angles. 

Not all of the ranges shown in Figures 8 and 9, 
corresponding to a given pull-up time, are feasible. 



10,000 50 0 0 0 

horizontal range (FEET) 


Figure 9. Curves of constant piill-np angles, F = .500 
feet/second, K = 3. 

For the Model 0 bomb director, pull-up angles less 
than al)out 12 degrees and pull-up times less than 
1.5 seconds are normally used. This restriction is 
chiefly a con.setiuence of the approximations made in 
deriving the eqtiations in Section 2.1.3. 

Because of the.se approximations, principally the 
omission of those terms in the .seiies for sin dp and 
cos dp which would result in terms of degree 3 or 
more in the eciuation for dp, the automatic computer 
determines a pull-up time which is somewhat too 
small. The con.seipience of an eai-ly release time is 
to cause the bomb to fall short of the target, as is 


















BOMB TOSSING 


15 


demonstrated, in an exaggerated form, in Figure 10. 
In the figure, P' represents the actual relea.se point 
and P the correct point. The Ijomb therefore crosses 
the colli.sion course OH at a point H' and hits the 
ground at a point K' short of the target H. Means of 
compensating for such errors are described briefly in 
Section 2.1.0, and in detail in Section 0 4. 

Denoting by an error in the determination 
of Tc, and by APp the error thereby caused in Tp, 


say 350 knots, all pull-ups conducted to the right 
of the 350-knot curve will have instrument errors 
less than 100 feet short of the target, while all 
pull-ups to the left will correspond to errors greater 
than 100 feet. The horizontal distance by which 
the bomb misses the target is approximately pro¬ 
portional to the cube of the range for a fixed velocity 
and dive angle.Consequently, the error increases 
rapidly when the maximum ranges of Figure 11 are 



Figure 10. Diagrammatic representation of toss bombing maneuver showing effect (exaggerated) of early release time. 


the bomb will cross the collision course a distance 
nearly equal to F • ATc from the target. This is 
true because the slant range is VT^. Since the arc 
H'K' of the trajectory is nearly a straight-line 
segment, it follows from the law of sines that 


sin dh sin (a -|- 6^') 

Equation (27) is basic in the error calculations con¬ 
sidered in Chapter 6. 

Figure 11 is a chart based on equation (27), from 
which can be determined all pull-up conditions 
which will result in a miss on the target 100 feet 
short. These curves represent theoretical opera¬ 
tional limits on the Model 0 bomb director if 100- 
foot accuracy is required. As will be seen from the 
figure, these maximum range curves depend on the 
velocity of the aircraft. For any given velocity. 


exceeded and decrea.ses rapidly for ranges less than 
this value. Figure 12 illustrates this for horizontal 
errors of 50, 100, 150, and 200 feet. 

The recommended operating limits, given in 
Chapter 1, are based on the curves of Figure 11 and 
have been found to be in close agreement with the 
results of field tests.Inasmuch as the limitations 
in range discussed in the preceding paragraph are a 
result of approximations used in solving the bomb 
tossing equations, it is to be expected that the 
mechanization of a more accurate solution of these 
equations would make possible longer maximum 
ranges. 

The first order solution on which the Model 1 
bomb director is based is a more accurate approxima¬ 
tion to the exact solution, so that it results in theo¬ 
retical maximum ranges which are somewhat greater 
than those of the Model 0 bomb director.'^® Further 











16 


THEORY OK 'HIE TOSS ME'rHOI) 



16000 


14000 


12000 


10000 


8000 


=> 

a 


(£ 

< 


6000 


16000 14000 12000 10000 8000 6000 4000 2000 

HORIZONTAL RANGE IN FEET (START OF PULL-UP) 


4000 


2000 


TARGET 


LJ 

O 

3 


_l 

< 


l'’u;UHE 11. Curv'es (theoretical) of maximum allowable ranges (for tlifferent aircraft velocities) corresponding to hori¬ 
zontal errors less than 100 feet, for bomb director Mark 1 Model 0 (xpo function). Example; if plane’s speed is 300 knots, 
bomb will hit ground 100 feet short of target if pull-up begins at any point (determined by dive angle) on the S-IO-knot 
curve, such as , 1 . Dive angle, 55 degrees, slant range 15,800 feet, altitude 13,000 feet. 








HOMIl TOSSING 


17 


60“ 



Figure 12. Curves (theoretical) of maximum allowable ranges corresponding to different horizontal errors for aircraft 
velocity of 350 knots, for bomb director Mark 1 Model 0 (i/'o function). If plane’s speed is 350 knots and dive angle 
is 50 degrees, bomb will hit ground 50, 100, 150, or 200 feet short of target for pull-ups beginning at D, A, F, or G 
respectively. 












18 


THEORY OF THE TOSS METHOD 


details of the corrections made in the Mark 1 director 
are given in Chapter 6 . It should be emphasized, 
however, that these theoretical maximum ranges 
may not be identical with the practical limits be¬ 
cause of the presence of other errors to be discussed. 
Practical range limitations have to be determined 
experimentalhx 

2 . 1.6 Instrumental Adjustments 

The two primary instrumental adjustments by 
means of which the impact point of the bomb may be 
changed are the meo7i point of itnpoct [MPI] adjust¬ 
ment and the stick-length offset. The diagrammatic 
location of these adjustments is shown in Figure 4. 
In the former, the slant range is changed by a fixed 
percentage yj'c/Tc, while in the latter, the range 
may be reduced by a fixed amount, i.e., by the 
amount Vi^Tc, where is a time ofi.set intro¬ 
duced by the stick-length offset circuit.^tui The AIPI 

dial may be used to bring the point of impact on the 
target as in flight calibration procedures, or in the 



Figure 13. MPI adjustment for bomb ballistic com¬ 
pensation (for bomb director Mark 1 INIodel 1). Ex¬ 
ample: for pull-up altitude of 6,650 feet, dive angle of 
60 degrees, and ballistic coefficient (C) of 2, MPI setting 
should be increased by 4/2 = 2 divisions. (1 division is 
equivalent to STc/Tc = 0.034.) 

tactical situation in which a miss is obtained on the 
first bombing run; or it may be used in correcting 
for the different balli.stic coefficients of the different 
types of bombs. 

Figure 13 is a chart of the AIPI adjustment for the 
Model 1 bomb director, which may be used for com¬ 


pensating for ballistic coefficient effects. From 
this chart it will be seen that this adjustment is 
constant for a fixed slant range and a given ballistic 
coefficient. For a fixed slant range, the MPI setting 
must lie increased when a bomli with a smaller 
liallistic coefficient is substituted for a bomb whose 
ballistic coefficient is larger. This is the case because 
liomlis with small ballistic coefficients are subject to 
gi'eater air resistance and tend to fall short. The air 
resistance effect may lie approximately compensated 
for hy an MPI adjustment of the amount 

1.73 X 10-® X-, (27a) 

Ta C 

where C is the liallistic coefficient and the slant 
range in feet. Figure 13 is liased on equation f27a). 

2 2 ROCKET TOSSING'^ 

Introduction 

The principles involved in the application of the 
bomb director to rocket to.ssing are essentially the 
same as for bombs. The differences in the theory 
and instrumentation are due to the fact that the 
high projectile velocit}^ results in a smaller angvflar 
drop from the direction of launching. This requires 
the u.se of a shorter pull-up time. 

In Section 2.2, the physical relations will be 
emphasized in the derivations of the formulas; more 
detailed and exact derivations will be found in 
Chapter 7. The theory applies to fin-stabilized 
rockets launched from “zero-length” launchers 
according to standard Navy practice. 

Rocket Trajectories 

The angular trajectory drops of rockets can be 
approximated by a linear function of slant range in 
the form m -f 7 ?/^. 169.170.172,174.177 The constants m 
and n depend upon the particular rocket type and 
propellant temperature, as well as plane velocity and 
dive angle. The constant m is essentially the drop 
occurring during the burning period and therefore 
depends upon the burning time in addition to the dive 
angle and airplane speed, whereas n is determined 
liy the trajectory after burning. 

‘^This section was prepared by I. H. Swift, formerly of 
the State University of Iowa, now at Naval Ordnance Test 
Station, Inyokern, California. 


ESTRICTK 














KOCKET TOSSING 


19 


The nature of n is indicated by the following 
considerations. The angular drop in radians of a 
projectile launched at an angle y with the horizontal 
and a velocity V + Vr, where V is the airplane 
velocity and T^ the velocity of the rocket relative 
to the airplane, is the ratio of the linear drop normal 
to the dive path to the coordinate along the dive 
path. Thus, if e is the angular drop and t is the time 
after launching. 


^gt- cos 7 


{y + yR)t + k^^sin 7 


cos 7 


■2(F+T«)2 


1 + 


gR 


(28) 


2(F+r«)2 


sin 7 


where R replaces the approximately equivalent 
quantity {V + Vit)t. This relation can be trans¬ 
formed as follows, where co is the drop at zero dive 
angle, 

^ QR cos 7 

2 (T + 1 -b 60 sin y 

= Ai> /? (1 — eo sin 7 ) cos 7 , (29) 


and 



The dive angle factor (1 — eo sin 7 ) cos 7 is the .same 
as that given in reference 215 and derived therein 
from geometric considerations. This shows that n, 
the trajectory drop per unit slant range, depends 
for a given rocket upon the velocity of the airplane 
and the dive angle. 

A more accurate expression for the trajectory drop 
of a rocket will now be indicated. The trajectory 
drop tables, published liy CIT for a number of 
rockets, 2 *®'-** have been fitted with an empirical 
formula of the type 

e = + (30) 

where a, h, and c are constants for a particular type 
of rocket, h{T) is a function of the propellant 
temperature T, and F{y) is a function of the dive 
angle 7 of the rocket which is defined graphically 
and is the same for all rockets. The values of these 
con.stants and formulas for the function h(T) for 


several types of Service rockets will be found 
Section 7.5. Equation (30) can be written 


-[ 


= Us- 


2V^- 


where 



(31) 


(31a) 


It is seen that the parameters enter in the first term 
of equation (31) in the same way they do in equation 
(29). The functions Ai and Ao play corresponding 
roles in the two formulas, as do F{y) and (1 — eo sin 7 ) 
cos 7 . 

Since formula (31) is ba.sed on trajectory calcula¬ 
tions which take into account air resistance, yaw, 
motion during burning, etc., it is a more accurate 
repre.sentation of the rocket trajectory than is 
equation (29). In addition, it includes a term which 
represents the effect of temperature variations of the 
propellant on the trajectory. 


Launching Characteristics 
of Rockets 

A rocket launched from a zero-length launcher has 
immediately after release a small velocity with 
respect to the airplane. As a result, the stabilizing 
action of the fins tends to cause the rocket to align 
itself with the airflow or flight line. Accordingly, 
it is assumed that the rocket leaves the airplane in 
the direction of the flight line at release. This 
assumption is further justified by the following 
con.siderations. In the usual in.stallation, the 
launchers are aligned with the boresight datum line 
and thus are about 25 mils below the flight line 
during the dive. During the pull-up, however, the 
angle of attack of the airplane increases. This tends 
to offset the angle which exists between the launchers 
and the flight line during the dive, resulting in a 
close enough alignment of the launchers and the 
flight line at release so that negligible error is intro¬ 
duced by this assumption. 

^ ^ ^ The Equation 

for the Pull-Up Time^^® 

An equation will now be obtained which determines 
the pull-up time, Tp, which will result in a hit. The 
equation will be set up with a delay time of 
seconds between the release of the rocket and the 












20 


THEORY OF THE TOSS METHOD 


ignition of the propellant; thus it is applicable not 
only to rockets launched from zero-length launchers 
(Td = 0), but also to the launching of large rockets 
in which a lanyard or a short time delay fuse is used 
to insure that the round is a safe distance from the 
airplane at ignition. The deiivation will make use 
of formula (31); in this way, account is taken of 
variations in propellant temperature. 

The following list itemizes the as.sumptions made: 

1. The target is stationary. 

2. The extension of the flight line beyond the point 
of initiation of pull-up intersects the target. 

3. The acceleration during pull-up is perpendic¬ 
ular to the direction of the flight line immediately 
preceding pull-up. 

4. The rocket leaves the airplane in the direction 
of the flight line at release. 

5. During the delay period, gravity is the only 
external force acting on the rocket. 

G. Yaw during the delay period has a negligible 
effect upon the motion. 



P'lGURE 14. Kepreseiitation of condition for liit 
(greatly exaggerated). From thi.s diagram, it may be 
seen that condition for hit is tliat pull-up angle dp be 
equal to angular trajectory drop c minus angle b. 

Figure 14 shows for the case of no-delay period 
the principal lines and angles related to the pull-up 
and the path of the rocket after release. 

From this sketch it is seen that a hit is obtained if, 
and only if, 

= € - 5. (32) 

This relation between angles is made to yield an 
equation for pull-up time by expres.sing both mem¬ 
bers in terms of the physical quantities which con¬ 
stitute the input to the director and the pull-up 
time. 

In radians, the angle b is given by d/R. The 
angle t is given by equation (31), but in order to 
allow for the gravity drop during the delay period 
between release and ignition, € must be increased 


by the amount gT^ cos a/Y, i.e., the ratio of velocity 
components perpendicular to and along the collision 
course. Thus, equation (32) becomes 

K = r V(y) + (33) 

L2I“ IJ 1 R 

In this formula, R is the slant range at the igni¬ 
tion point and is nearly equal to the quantity 
V{Tc — Tp — T,i). In the small terms {gTa cos a/V) 
and d/R, it is sufficiently accurate to take VTc for R 
and to replace cos a by F(y). This permits equation 
(33) to be written in the form 

- r„ - T,,) + 

Zi \ I 

+ . (34) 

V VT, 

where = Fiy). 

As in Section 2.1, the pull-up angle, 9p, is given Ijy 

Op = ~ f {K — cos a) df. (35) 

V Jo 

The distance d is given hy the double integral 

— cos a) J dt. 

When these are substituted into equation (34), that 
ecpiation becomes 

^ |^/\ — cosa + (A' — cosa)f//Jd( 

= + rd(2 - .4,) 1. (36) 

A 2 L g J 

The inner integral Jo (K — cos a)dt will now be 
approximated. For this purpose, the expression 
K — cos oc will be replaced by pt, where p is a constant 
time rate of change of K during pull-up. This is 
justifiable since (1) in the normal pull-up it has been 
found that rockets are released while K is still in¬ 
creasing, (2) K increases nearly linearly, and (3) the 
term in which this replacement is made is small in 
relation to the terms to which it is added. It follows, 
then,that 

f (K — cos a)dt = f ptdt = \ ptr, 

Jo Jo 

and 

rijy - 'f 






ROCKET TOSSING 


21 


From equation (32) of Chapter 7, 

P 

Hence, 

f f (K - cos a) puh r r 

Jo Jt) 6 


-f 




When this result is put into equation (30), it is found 
that the relation can be written in the form 


2 

.42 


i: 


(/v - cos a + lA.xPii)dt 


= ^ r - + r,(2 - .4=)]. (37) 

^42 L <7 J 

This equation is fundamental for the bomb director 
as applied to rockets. 

The bomb director measures the quantities K, a, 
and Tc. It must now be made to integrate the quan¬ 
tity (K — cos a + 2.42iAfl/3) in a satisfactory manner. 
The number .42, or .4 factor, depends upon the type 
of rocket and the velocity of the airplane. It might 
appear, therefore, that the equipment for rocket 
tossing shortld measure also the velocity of the 
airplane. This is found not to be necessary since the 
.4 factor is set for a median airspeed and any varia¬ 
tion from this median velocity is partially compen¬ 
sated by anopposite error resulting from the change 
irr angle of attack; this will be referred to again in 
Sections 2.2.9 and 2.2.10. The final result, as proven 
by field tests (see Section 5.3), is that the equipment 
is insensitive to variations in airplane velocity. 


^ ^ Comparison with Tp for Bombs 


In order to comj^are the pull-up time for a rocket 
with that for a boml) released irnder similar condi¬ 
tions, the left-hand member of equation (37) may be 
wi'itten 

2 _ 

[A — cos a + ^Ao^rYI'p, 


wheie K is the time aveiage of K from the beginning 
of pull-up until the release of the rocket. This per¬ 
mits eriuation (37) to Ire written as a linear eciuation 
for Tp, and the solution of that eriuation is 


.1 iJrTcA ’/'/? r ^ + T,/(2 — . 12 ) 
_ 1 - (J _ 

2[/v — cos a + IAo^r] 


(38) 


In order to effect the comparison, the temperature 
term will be omitted, and 7b will Ire taken as zero. 
Equation (38) becomes 

T = J^2'^r'1c _^ 

^ 2(/v — cos a -t- lA-id/R) 

The corresponding formula for bombs is 

'V - 

K + V A'2 _ K 

Recalling that 4/r = F{y), the similarity of these 
two formulas provides the justification for the nota¬ 
tion xj/R and for regarding F{y) as the function for 
rockets. This function is discussed in more detail in 
Section 7.2.8. The graphs in Figures 15 and 16 
show how the values assumed by \pi for bombs and 
\pR for rockets differ. 

The denominator /v + V K~ — K is very nearly a 
linear function of K, being represented well by 
2{K — 0.3) for the range of values of K occurring in 
rocket tossing. Thus, it is seen that the two de¬ 
nominators are essentially the same. The chief 
difference in the two formulas is the presence in 
equation (39) of the factor A^. It has a value be¬ 
tween 0.1 and 0.35, depending upon the type of 
rocket and the airplane velocity.^^® 


Mechanization of the 
Rocket Tossing Equation 


Equation (37) is the relation upon which the 
instrumentation is to be based. In this article, the 
temperature variations of the propellant and the 
effect of the delay period will be ignored. They are 
treated in detail in Section 7.5. The relation to be 
mechanized is therefore 

- - / (/v — COSO! + lA2^pR)dt = ^rT,. (40) 

.4 2 Jo 

The iMark 1, Model 2, bomb-rocket director 
(Section 3.3) accomplishes the solving of the above 
equation with a few modifications to the circuit used 
for bomlrs. The principal modification is the provi- 
.sion for introducing the A factor. 

The eciuation actually scjlved by the computer is 


2 /'’> m 

.ul 


where /?(/) is a resistor whose value is determined 
l)y K. 

From examination of the circuit constants for the 












22 


THEORY OF THE TOSS METHOD 



Figure 15. Comparison of F{y) (i/' function for rockets) withi/'i for bombs. F{y) curves are for 5.0-inch HVAR; bomb 
function ypi is for Tc/V = 0.03. Plane velocity = 500 feet/.second. 



Figure 16. Comparison of F{y) (\p function for rockets) with i/'i for bombs. F{y) curves are for 11.75-inch aircraft 
rockets; bomb function i/'i is for = 0.03. Plane velocity = 500 feet/second. 











ROCKET TOSSING 


23 


Mark 1 , Model 2 , director, it is evident that the 
resistor R(t) should satisfy the equation 

p;/Q 

R{t) = — - ' megohms. (41) 

K — cos a + iA 24 'R 


This choice of R(t) will result in computer per¬ 
formance in accordance with equation (40). 

The actual construction of R(t) provides that 


R{t) = 


-when cos a <K< 1.3 

3^2 


10/3 

K + ylK- - K 


when 1.3 < 


A'. 


Consequently, the equation actually solved by the 
computer is 

^ 1 . 3 '/' d —~ f [K ^K- — K] dt = l\\l/, (42) 

where 7’i 3 is the time at w hich K equals 1.3. 

The integrands in equations (40) and (42) will now 
be compared. For convenience, w'rite 


Fii(K,a, A) = 2(A - cos a + IA4r)- 

Then, replacing ypn by cos a, to which it is roughly 
equal, 

F{i{K,a,A) ~ 2K — 2 COSO! (1 — §^ 2 ). 

A median value 0.825 of cos a is selected, corre¬ 
sponding to a = 34.4 degrees, so that Fii{K,a,A) 
becomes 

Fr{K, A) = 2K - 1.65(1 - IA 2 ). (43) 


As a result of this simplification of Fr, the pull-up 
time determined l)y the computer will be too short if 
a < 34.4 degrees and too long if a > 34.4 degrees. 
This error is compensated for by use of the\p function 
for boml)s. As seen from Figures 15 and 16, \pR > 
if Of > 34.4 degrees. Consequently, the right-hand 
member of ecjuation (42) is somewhat too small, 
leading to a value of Tp as determined by the com¬ 
puter wdiich w'ill l)e too small. In the same way, 
for small dive angles, a similar compensation occurs. 

If A 2 is taken ecpial to unity in equation (43), an 
expression essentially equal to A -f VA- — A is 
obtained. The following table show's the close agree¬ 
ment between these functions. 


K 

K + Vk- - K 

Fb(A,1) 

Difference 

1.3 

1.92 

2.05 

0.13 

2.0 

3.41 

3.45 

0.04 

3.0 

5.45 

5.45 

0.00 

4.0 

7.46 

7.45 

— 0.01 

5.0 

9.47 

9.45 

— 0.02 

0.0 

11.48 

11.45 

— 0.03 


The A Factor 

In Section 2.2.2 tw'o expressions w'ere given for 
the A factor, namely 



g 


Graphs of these tw'o expressions show^ that for the 
ranges of the parameters occurring in rocket tossing, 
each is nearly linear in V. A comparison of numerical 
values furnished by these formulas is given in 
Section 7.4.4. 

Both AI and A 2 are to be compared with an A 
factor determined experimentally. Satisfactory agree¬ 
ment has been obtained betw'een the theoretical and 
the experimental values (see Section 7.4.5) except 
in the case of the 11.75-inch AR, for w'hich the 
experimental A factor is about 40 per cent larger 
than the theoretical value. The reason for this dis¬ 
crepancy is presumed to lie in conditions obtaining 
at the release of the rocket. 

^ ^ Compensation for Propellant 
Temperature and Lanyard 

Firing Delay Time. Experimental tests tossing 
the 5-inch HVAR show^ approximately a 15-mil shift 
in mean impact point as the propellant temperature 
is varied from 0 F to 100 F, other variables being 
kept the same.^^^ It is evident, therefore, that this 
variable must l^e taken into account. The trajectory 
mil drop occurring before firing with a lanyard is 
of the same order of magnitude as the mil drop due 
to extreme temperature variations. Both of these 
drops are to be added to the mil drop after burning, 
and both are independent of range; it is precisely 
these drops w'hich determine the value of m in the 
expression m + nR for total mil drop. In fact, 
adding the part of equation (30) w'hich pertains to 
temperature to the gravity drop during the delay 
period results in the formula 

m = ^ ^ ^ [c/,(r) + gT^l 

I' I 

The temperature and lanyard control on the 
Mark 1, Alodel 2, bomb director^*® provides for the 
term m. This control is a potentiometer across the 
output of the gyro. The voltage from the control is 












24 


THEORY OF THE TOSS METHOD 


used in the circuit to increase the pull-up time, and 
consequently, the pull-up angle by the amount m 
mils. The increase in pull-up angle obtained is 
proportional to \{/ since the voltage is obtained from 
the gyro and inversely proportional to airplane 
velocity because the rate of change of pull-up angle is 
proportional to 1/T. 

A more complete discussion of the theory and 
operation of this control, together with calibration 
data and comparison with field results, is gT’en in 
Section 7.5. 

^ ^ ’ Shift of Impact Point 

with the A Factor 

In equation (33), the term which shows the great¬ 
est variation when the A factor is changed and the 
other parameters kept the same is the term in Ao. 
Accordingly, a change of amount dA in the A factor 
results in a change in pull-up angle given by 

ddp(m[\s) ^ dA X lOh (44) 

Since the rocket trajectoiy deviates but little from 
the flight line at release, the mil error at the target 
will be nearly equal to the change in pull-up angle. 
Thus, equation (44) may be used to find the angular 
shift in impact point at the target resulting from the 
change dA in the A factor. 

Formula (44) shows that the effect on mil error of 
increasing the A factor slightly is proportional to the 
range, inversely proportional to the square of the 
airplane velocity, and in such a .sense that the shot 
falls long. For R = 2,300 yards, a = 35 degrees, 
V = 320 knots = 540 feet/second, a change of 0.01 
in A corresponds to an error of 2.8 mils at the target. 
An experimental check at Inyokern with the 5.0-inch 
HVAR fired from an F4U-1D gave a shift of 2.2 mils 
under the same conditions.This is regarded as 
satisfactory agreement with the theory. Roughly, a 
change in A of 0.01 shifts the impact point 1 mil per 
thousand yards slant range. 

2 2.10 Shift of Impact Point 
with Plane Velocity 

In the Model 2 rocket tossing equipment, no 
provision is made foi- measuring and taking into 
account the plane \'elocity. Instead, a mean value 
of the airplane velocities expected to be u.sed is set 
into the eciuipment. A considerable variation of 
airplane velocity from the present value will be shown 


in this section to have little effect upon the overall 
disper.sion; i.e., the equipment is insensitive to 
airplane velocity. 

Except for smaller terms, the angle 8 (see Figure 
13) is given by 


8 = e — dp = aR xpjie ^ 


ijA 2R4'R 

2 F 2 


If V is increased to V' and a corresponding increase 
made in A 2 so as to secure a hit, the new 8 will be 
given by 

6 ' = nRiKe-''’'" - . 

2r'‘ 

If, however, A 2 is not changed, the angular drop of 
the rocket from its line of motion at release will still 
be aR\pf}e~^'^'', but the pull-up angle will now be 
gAoR^'n/^y''- The failure to increase A 2 results in 
the rocket’s falling .short, the angular error being 
given by the negative quantity 


21 ^'- 


(45) 


Since the angle of attack of the airplane during 
the dive is given by'^ 

nr cos a 


r- 


_ (’' 214 


the change in angle of attack caii.sed by increasing the 

velocity by the amount dr = r' — IMs 

, 2nrcos« ,,, 

(in = —- d\ . 

yn 

In order to keep the .sight line on the target, this 
requires a rise in the flight line of amount 

2 nr cos a 


yn 


‘ d\\ 


(4(1) 


and the direction of motion of the rocket upon 
release is elevated by this amount. Combining 
equations (45) and (4(1) gives for the total change in 
the pull-up angle 

^ 2CA cosa ^^^. _ cfR^Pii ^ 

p yn 2V'- 

Since 


.42 =- 


it follows that 




In thi.s disc*us.sion, no differentiation is made between 
indicated airspeed and true airspeed. 











TORPEDO l()SSI\(; 


25 


and thus equation (47) becomes 
, r2C]r cos q; fj, 1 / I 

=[ - - 



(48) 

Figure 17 shows a graph of ddp/dV, that is, of the 
rate of change of mil error for each foot/second 
change in airplane velocity. In the construction of 


~ 0.25 



VELOCITY (FT/SEC) 

pyauRE 17. Rate of change of rocket impact witli 
airplane velocity. (Computations are based on range 
of 7,680 feet, dive angle of 3.5 degrees, and constants for 
PT)F-5 airplane and .5.0-incli IIVAR.) 


this graph, a dive angle of 35 degrees was iLsed and a 
range of 7,680 feet was assumed, and the other con¬ 
stants are those of an F6F-5 airplane and the 5.0-inch 
HVAR. This graph shows that a change of 10 feet/ 
second in airplane velocity causes a shift of less than 
]/2 iit impact error. 



FiGTOtE 18. Rocket impact error as function of air¬ 
plane velocity when sight is calibrated at 608 feet/ 
second. (Computations are ba.sed on F6F-5 airplane 
and 5-inch IIV.\R, slant range of 7,680 feet, and dive 
angle of 35 degrees. Zero error is assumed for airplane 
velocity of 608 feet/second. Isolated j)oints represent 
data from field tests using same type of airplane and 
rocket. 


Figure 18 shows the theoretical mil error for a slant 
range of 7,680 feet and a dive angle of 35 degrees, 
again with an F6F-5 airplane and the 5.0-inch 
HVAR. The graph was obtained by computing the 
integral of equation (48) with the constant of inte¬ 


gration chosen so that the error would be zero at 
360 knots = 608 feet/second. The isolated points on 
the graph are from data obtained at Inyokern with 
the same combination of airplane and rocket. 
Within the accuracy of the test, the agreement with 
theory is satisfactory. In this typical ca.se, the graph 
shows that a .shift in velocity of about 30 feet/second 
or 18 knots is re(iuired to produce a shift of 1 mil 
at the target. 

The fact that the MPI shift with velocity is small 
does not mean that the A factor need not be set 
accurately. It means that when the A factor has 
been correctly set so as to produce a hit, then a 
small change in the velocity of the airplane will not 
lead to large errors at the target. 

2^ TORPEDO TOSSING" 

In the normal method of releasing torpedoes from 
aircraft, the distance by which tlie torpedo falls 
short of the target may be as much as 3,000 yards. 
As a consequence, the total travel time of the torpedo 
in the water is large, and the target may have suffi¬ 
cient time to engage in evasive maneuvers. In order 
to reduce this travel time to a minimum, it is desired 
to be able to locate accurately the point of impact of 
the torpeflo in an interval between 450 and 900 feet 
short of the target. This minimum distance short is 
re(iuired to allow sufficient water travel to arm the 
torpedo. 

44ie bomb director may be utilized to toss tor¬ 
pedoes by introducing instrumental^ a of 

such an amount as to cau.se the torpedo to fall the 
required distance .short. The ATc required to place 
the torpedo exactly 450 feet short for a toss bombing 
maneiu’cr initiated at a dive angle of 25 degrees and 
at a second altitude point of 1,395 feet was computed 
and found to be 3.719 seconds. Using this value of 
ATc, the minimum and maximum altitudes were 
determined for dive angles between 15 and 25 
degrees, such that the torpedo falls between 450 feet 
and 1,350 feet short of the target.'*'’ The results are 
summarized in gi'ophical form in Figure 19, vacuum 
trajectories bemg plotted. This makes it possible to 
approximate visually the angle of release of the 
torpedo with respect to the horizon, the angle of 
entrance into the water, the distance short from the 
target, and the limits on range and dive angle. In 
the figure, the lower area shaded with the single 

e Sections 2.3 and 2.4 were written by Dr. Albert London, 
of the National Bureau of Standards. 









26 


THEORY OF THE TOSS METHOD 


diagonal lines includes all toss bombing pull-ups ever, practically all of them may be classified under 
for which the torpedo will have an impact point two main headings: 

\\ithin the interval of 450 to 900 feet short, while the 1. Methods involving special sighting procedures, 

upper cro&s-hatched region corresponds to an interval 2. Instrumental methods which compute the 



NOTE ; DISTANCE FROM TARGET IN FEET. 

Figure 19. Torpedo tossing ciiart (vacuum trajectories) for 1' = 250 knots, K = 3, and ATc = 3.719 seconds. Area 
shaded with single diagonal lines shows range of values of dive angle and second altitude which will j)lace torpedo 450 
to 900 feet short of target; cross-hatched area corresponds to interval of 900 to 1,350 feet. 


of 900 to 1,350 feet short. It should be emphasized 
that these areas on the graph represent the limiting 
values of the second altitude point, and initiation of 
the dive occurs, of course, at correspondingly higher 
altitudes. All important physical quantities may be 
read from the gi’aph. The values of some are tabu¬ 
lated in the table below for I^ = 250 knots, K = 3, 
and ATc = 3.719 seconds. 

2 4 W IND CORRECTION 

‘ Toss Bombing: 

W iiid Correction Procedure 

In order to compensate for the effect of wind, a 
number of different methods are available. How- 


magnitude of the wind and automatically make the 
required correction. 

Sighting jVIethod 

In the sighting method of compensating for wind, 
if an estimate of the magnitude and direction of the 
wind is not available, a preliminary bombing run 
may be made. The mil errors, both in range and 
deflection, are noted and on the second run, the 
aiming point is changed to correspond to the ob¬ 
served error in the first run. An application of this 
principle is the squadron method in which a group of 
planes all make the same approach on a target. The 


Dive 

angle 

(degrees) 

Second 

altitude 

point 

(feet) 

Pull-up 

altitude 

(feet) 

Slant 

range 

(feet) 

Release 

angle 

(degrees) 

Entrance 

angle 

(degrees) 

Impact 
point from 
target 
(feet) 

25 

1,395 

1,210 

3,301 

— 20 

37 

450 


2,880 

2.880 

6,760 

— 9 

44 

887 


4,150 

4,150 

9,820 

— 1 

50 

1,362 

15 

1,395 

1,360 

5,390 

— 2 

34 

900 


2,000 

2,000 

7,727 

6 

41 

1,361 


LTIICT 















WIND CORRECTION 


27 


first plane makes the preliminary run. The following to construct similar sighting charts for any type of 
planes note the impact point and change their aim sight reticle. In this method of sighting, the bombing 
accoidingly. Experimental results obtained by this run is made, keeping the target located at a fixed 
method show a marked improvement in accuracy. point in the sight field. This point will be the center 


TAILWIND 

lecf 



1 

0 * 

HEADWIND 

FiGURPi 20. Wind correction chart for 40-degree dive angle, with superimposed Mark 8 gunsiglit reticle. (See text for 
directions as to use.) 


If the magnitude and direction of the wind relative 
to the intended dii-ection of approach of the air-plane 
are krrown approximately, it is possible to irse the 
sighting grids, an example of which is shouTi in 
Figure 20, to determine the aiming point reqrrired. 
These wind correction charts are drawn with the 
Mark 8 girnsight reticle sitperirnposed. It is possible 


pip of the sight in the zero-wind case only. If this 
aiming point is used, a collision cottrse approach will 
be established for the bombing rirn. Instr-irctions 
for using the charts follow: 

1. Select the wind-correction chart corresponding 
to the approximate dive angle at which the toss 














28 


THEORY OF THE TOSS METHOD 


bombing maneuver is to be conducted. (Figure 20 
is for a 40-degree dive angle.) 

2 . The wind-correction ellipses on the chart 
coriespond to different values of the ratio of wind 
velocity to airplane dive velocity, each ellipse 
corresponding to a fixed value of this ratio. Thus, 
if the wind velocity is 30 knots, and airplane velocity 
300 knots, the ratio is .10 and the ellipse mai ked .10 
should be used. 

3. The required sighting point may then be de¬ 
termined from the direction of the wind relative 
to the intended heading of the airplane in the di\'e, 
this point being determined by the intersection of 
the wind-airplane ^'elocity ratio ellipse with the 



Figure 21. Nomogram to determine ratio of wind 
speed to airspeed. (To use, set straiglit edge through 
proper values of wind speed and airspeed in tlive and 
read off ratio. Speeds are in knots.) 

wind direction radius. Thus, if the ratio is .10 and 
the direction of the wind is 15 degrees relatitT to the 
heading of the airplane, the target should be kept 
fixed in the sight at the point which is the inter¬ 
section of the .10 ellipse with the 15-degree lino. 


4. The pull-up should be made in the vertical 
plane; i.e., the target or aiming point should move 
dowTiw’ard in a direction parallel to the vertical line 
of the sight reticle. 

Figure 21 is a nomogram which may be used for 
determining the ratio of wind velocity to airplane 
velocity. A mathematical discussion of the nature 
of the wind correction grids is given in Section 0.6. 

The same grids may be used in firing rockets if 
the plane velocity is replaced by the final rocket 
velocity in computing the value of the wind-pro¬ 
jectile velocity ratio. A nomogram similar to that of 
Figure 21 can be used to give the desired ratio as a 
function of rocket type and wind velocity. It is 
(issiimcfl that the speed of the plane is 375 knots, hut 
the results can he applied with negligible error at other 
speeds. Having determined the appropriate ratio, 
the correction is made as in the case of bombs.i*- 

2 .4..? Instrumental Alethod of 
Wind Correction 

The instrumental method of correcting for wind 
(or eciuivalent target motion) was in its iireliminary 
developmental stage at the end of the war. At that 
time it had been proposed to compensate for range 
winds only, i.e., head or tail winds. In this method, 
the pilot flies a pursuit course, keeping his sight pip 
fixed on the target. Conseciuently, in the presence 
of wind, the flight path is curved, the dive angle 
varying with time. The rate of change of dive angle 
with time is measured by a rate-of-turn or pitch gyro 
and is a function of the wdnd velocity. The voltage 
output from the gyro may be used to decrease or 
increase the no-wind bomb release time by the 
amount necessary to obtain a hit. Further details 
of this method will be found in Chapter 0. 








Chapter 3 

INSTRUMENTATION" 


INTRODUCTION 

HE OPERATION of the boml) director Alark 1 
Model 1, AN ASG-10, which provides for lioml) 
and toipedo tossing, and of the bomb director Mark 1 
Model 2, AN ASG-lOA, which provides also for the 
tossing of rockets, is described in Sections 3.2 and 3.3. 
The pilot ])roduction units which were designated 


Problems connected with the actual construction 
and assembly of the bomb director are discussed in 
Section 3.5 and, with lalioratory te.sting, in Section 
3.6. 

The most advanced developmental work which 
did not reach the stage of production by the end 
of the war is given in Chapter 8. 



GYRO CONTROL BOX ALTIMETER 



Figure 1. liomb director Mark 1 Model 1 AX/ASG-10, comiionents and inteninit cabling. 


as Mark 1 Alodel 0, AN/ ASG-10(XN) are described 
briefly in Section 3.4 and further in Section 3.5. 
The circuit diagrams changed considerably during 
development, but the operating principles which are 
embodied in the Mark 1 Model 1 and Mark 1 Model 
2 circuits are essentially the same as in the Mark 1 
Model 0. (Detailed instructions as to installation 
and maintenance of the bomb director IVIark 1 
Model 0 are given in reference 220; of the bomb 
director Alark 1 Alodel 1 in reference 232c.) 

:i Chapter 3 i.s based on material compiled by V. W. Cohen 
and F. M. Defandorf, of the National Bureau of Standards, 
and on the final report of the Magnavox C'ompany .202 


3 2 BOMB DIRECTOR MARK 1 MODEL 1, 
AN/ASG-10 

^ ‘ Assembly 

The bomb director Alark 1 Model 1 consists of an 
altimeter unit, a gyro unit, computer, control box, 
switch box, and an indicator lamp which are electri¬ 
cally interconnected by cables. Figure 1 shows a 
sketch of the components. A functional diagram 
of its circuit is given in Figure 2. This eciuipment is 
so designed that it determines the reciuired release 
instant on the basis of the time to target 7’^, the angle 
of dive a, and number of gr’s pull-up acceleration K. 


^r ^E8TRTT^rn, 


29 






















































30 


INSTRUMENTATION 


The manner in which it performs this operation will around the periphery of the dial extending from an 
be discussed by describing the function of each unit altitude indication of 10,328 feet down to 1,390 feet 
separately, starting with the altimeter. in steps which are in the ratio of 6 to 5. The contacts 



Figure 2. Functional circuit diagram of bomb director Mark 1 Model 1, AN/ASG-10. 


Altimeter Unit jVIark 1 Model 1, 
ID-112 ASG-10 

The altimeter unit supplies the electrical computer 
with time-to-target information. The instrument is a 
Kollsman sensitive altimeter which has been mod¬ 
ified through the addition of a fine ribbon contact 
on its 1,000-foot hand and a series of contacts 


on the altimeter may be seen in Figure 3. In Figure 3 
the Model 0 altimeter is shown with the glass face 
removed to show the fixed contacts around the 
periphery. There is no significant difference between 
the Model 0 and Model 1 altimeters. As indicated in 
Figure 2 the operations within the altimeter consist 
in merely grounding the various altitude points. 
Discussion of subsequent operations is given in 


















































































































BOMB DIRECTOR MARK 1 MODEL 1 


31 




Section 3.2.4. In all cases the altimeter is preset to 
indicate altitude above the target to be attacked. 
Thus, for a imiform-speed constant-angle dive, the 
elapsed time between any two altimeter contacts 
will be one-fifth the time it would take the plane to 
reach the target from the second-altitude point. 


Figurk 3. .\ltimeter unit, Mark 1 Model 0, with 
cover ^lass removed. Note fine ribbon contact on 
1,000-foot liand and contacts on rim at following alti¬ 
tudes: 1,390, 1,668, 2,002, 2,402, 2,882, 3,459, 4,151, 
4,981, 5,977, 7,172, 8,607, and 10,328 feet. Model 1 
(see assembly drawing. Figure 1 of C'hapter 4) is essen¬ 
tially same as iModel 0. 

^ Gyro Mark 20 Model 1, 

MX-329/ASG-10 

The gyro furni.shes the intelligence related to the 
angle of dive. It is a Sperry Artificial Horizon 
indicator with a (iO-degiee sector of a circular 
tapered wire-wound potential divider mounted 
inside its case. Contact with the resistance strip is 
made through a contact arm mounted on the gyo-o’s 
ginibal ring and operated liy a solenoid in the arm¬ 
ing circuit of the plane. A modified gyro is .shown in 
Figure 4. The resistance strip, commonly referred 
to as the \j/ card, is composed of three linear segments 
(see Section 6.3.3) and is so designed that it provides 
the required dive-angle correction for a plane speed 
of 500 feet/second. A \p card in various stages of 
assembly is .shown in Figure 5. Adjustment to 
compensate for other plane velocities iTJV correc¬ 
tions) is made through a variable resistor which is 
connected in series with the strij). This adju.stment is 


Figvrk 4. Gyro Mark 20 Model 0 (XN2), shock- 
mounted and e(iuii)j)ed with electric motor for caging and 
uncaging. Model 1 (see assembly drawing, h’igure 1 
of Chaider 4) is essentialfi^ same as Model 0. 

not ci-itical since the factor is mainly a function 
of the dive angle and varies only slightly with plane 
speed. It is not intended to adjust this control 


Figure 5. A 3-step wire-wound xp card in two stages 
of a.ssembly. At bottom left is shown straight wire- 
wound card; above it is shown card after it has been 
heat-formed to proper radius. .\t t(»p left is molded 
bakelite card holder. At right is xp card mounted on 
holder. 









32 


IN STRUM EN TATION 


(‘xcept in such extreme cases as woultl result when 
cl^anging the etiuipment from fighters to toipedo 
l)oml)ers. 

The instrument is uncaged in level flight before 
the plane enters the dive toward the target. When 
the pilot closes the lx)ml) release switch to start 
computer operation, the gimbal arm contact is 
brought into contact with the resistance strip. 

^ Computer Mark 20 Model 1, 

CP-15 ASG-10 

The computer combines the information from the 
<lifferent intelligence sources and automatically 
t riggers the boml) relea.se circuit at the pi'oper time. 



Figurk 6. Accelei’ometer (jr /v-block as.sembly of 
Model 0 computer, showing spring-supported weight 
(or bob) in position. Contact carried by bob (see 
Figure 7) slides over segmented commutator (or K 
block) connected to network of precision resistors. 

One intelligence source, the acceleration integrator, 
is so intimately related to the computing action that 
it is built into the complete unit and generally is 
considered part of it. 

Acceleration is indicated by a spring-supported 
weight, such as is shown in Figure 6. The weight 
carries a sliding contact over a commutator block ' 


(generally called the K block) consi.sting of 83 insu¬ 
lated metal disks. The.se are shown in Figure 7, 
which is another view of the object shown in Figure b, 
but with the spring .supported weight remo^'ed. The 
segments of the commutator are connected to a 
network of precision lesi.stors (shown in Figure (>). 
Figure (1 is actually of a Model 0 computer, but the 
basic opeiations are the .same as in the Model 1. 
The latter is .shown in Figure 11. 

The computer as.sembl.v contains, in addition to 
the acceleration integratoi, the timing capacitors, 
the altimeter circuit and relea.se circuit thyratrons, a 
dynamotor which sui^plies 285 volts d-c, and relay's. 

The sequence of opeiations in the computer is as 
follows: (all circuit references are to Figure 2). 

1 . Placing the power switch in the OX position 
starts the dymamotor, heats the cathode in each of 
the thy'ratrons, establishes the proper thyu-atron 
grid bia.ses, and places 150 volts between theO-degree 
position on the gyro resistor and ground. This 



Figure 7. Another view of /v-block assembly with 
spring-actuated weight removed to show commutator 
segments. 

switch is clo.sed far enough in advance of the dive 
to enable circuit elements to become stabilized. 

2 . Closing the bomb relea.se switch operates 
relay No. 1. This energizes the gyro solenoid, applies 
+ 285 volts to the plate of the altimeter tlyvratron, 
and operates the l>ob latching solenoid to fiee the 
acceleration bob. 

^ 3. The actual computing operation starts at the 

















BOMB DIRECTOR MARK 1 MODEL 1 


83 


first altimeter contact following the closing of the 
bomb release switch. The altimeter hmid ribbon, in 
sweeping across this peripheral contact, fires the 
thyratron by grounding its cathode and thereby 
dropping its potential momentai'ily to a potential 
which is several volts below the potential of the grid. 
The resultant plate current oi^erates relay No. 2 
which removes the short from the first G-mfd capac¬ 
itor, Cl, and applies the gyro output voltage to it 
through a resistance having a nominal value of 
2/3 megohm. (In the Model 0 this capacitor as well 
as ('•> had a 2 -/jf value.) Relay No. 2 simultaneously 
operates relay No. 3 which locks relay No. 2 and 
(luenches the thyratron by bieaking its plate circuit 
l)riefly at the 3A contact. Relay contact 3 A again 
applies -f 285 volts to the thyratron plate. 

4. AVhen the second altimeter contact is made, the 
thyratron again fires because its cathode is grounded 
momentarily. The resultant plate current now 
operates relay No. 4. This applies current to the 
signal lamp notifying the pilot to commence pull-up. 
It simidtaneously ungrounds the negative side of 
condenser Ci (isolating its charge), removes the 
short from the second fi-mfd capacitor C 2 , and 
connects one side of the latter to ground (except for 
the small amount of bias jjroduced by the stick- 
length offset). The charge acquired by Ci was 
acquired during the time it took the plane to travel 
between the two altimeter points; hence, it is pro¬ 
portional to 1\- Since the negative side of this 
capacitor is connected to the grid of the release 
circuit thyratron, and the mid-point between Ci and 
('2 is essentially at ground potential through Co 
at this instant, the voltage associated with the abo\’e 
charge lowers the thyratron grid a corresponding 
amount below ground. Relaj^ No. 4 furthermore 
operates relay No. 5 which causes the charging 
current to capacitor C 2 to pass through the K block 
circuit who.se resistance is nominally 10/3 megohm. 
At the .same time relay No. 5 puts + 150 volts on 
the plate of the release circuit thyratron. 

Should the dive continue toward the target with¬ 
out pull-up, the.se two equal capacitors will have 
ecpial charges when the target is reached, since the 
same charging \'oltage would be used for both, while 
the resistances of the two circuits bear the same ratio 
as the corresponding charging times. As the charge 
(m C-i increa.se.s, the thyratron grid becomes less and 
less negative, the difference between the voltages 
on the two capacitors being proportional to the 
remaining time to target. 


5. When {)ull-up begins, the K block bob move.s 
downward untler the action of the irnpo.sed pull-up 
accelei-ation. This ai)i)lie.s the 15()-volt supply 
directly to one of the K block segments through the 
contact attached to the l)ob. The resistors connected 
to the K block are chosen so that for an acceleration 
of N< 7 ’s, the effective resistance in the circuit is 

10 

- - =zz.- megohm. 

3 (A -f VA '2 - at 

The thyratron fires when the chai-ges accumulated 
on the two capacitors become equal at 7/, seconds 
and the following equation is sati.sfied: 

V7v2 - K) (It = 7/iA. 

(See Section 2 . 1 .) 

6 . Firing of the release circuit thyratron operates 
two relays. No. G and No. 7. The latter energizes the 
bomb release mechanism and at the same time frees 
the gyro arm contact. No. G extinguishes the .signal 
lamp to indicate that the bomb has been released. 

7. Consistent computer operation is assured by 
means of the following provisions, (a) Firing of the 
altimeter thyratron by closing the bomb release 
svitch while the altimeter ribl)on is on a jjeripheral 
contact is prevented by the 0.25-mf capacitor in the 
altimeter-cathode lead. Closing the altimeter con¬ 
tact quickly charges this capacitor and prevents the 
passage of another pulse until the altimeter contact is 
open for about 0.3 .second. If the altimeter contact 
closes before plate voltage is applied to the thyratron, 
the thyratron will not fire until the next altitude 
point is reached. This capacitor also prevents more 
than one pulse per contact since it retains its charge 
for sufficient time to allow the altimeter hand to 
travel completely acro.ss the contact, (b) A 0.3- 
megohm resistor placed between the 150-\"olt terminal 
and the gyro contact arm insures that the computer 
will receive a chai-ge coi responding to a 40-degree 
dive angle in ca.se of any failure in the g.vro circuit, 
(c) Releasing the bomb release switch at any time 
prior to bomb release automatically re.stores the 
circuit to its normal standby condition. 

Control Box Mark 8 Model 1, 

C-200 ASG-10 for Console Installation, 
C-203 ASG-10 for Other Installations 

This unit hou.ses switches and controls operated 
by the pilot as follows: 

1 . A sii'Uch to cage, or uncage the gyro ek'ctrically. 




34 


INSTRUMENTATION 


2. A momentary test switch. This provides the 
pilot with a check on the operation of the computer. 
The switch is wired across the altimeter contacts. 
If the equipment is operating pioperly, it should 
reciuire five times the time between two operations 
of the switch to release the bomb. 

3. Stick-length offset. This adjustment is used in 
releasing a stick of bombs to cause the first bomb 
to hit short of the target. It imposes an initial 
positive bias on the second capacitor. This shortens 
its charging period by a definite time and produces 
the desired reduction in Tp. One position of this 
switch is used for torpedo tossing. This control is 
shown in simplified form in Figure 4, Chapter 2. 

4. MPI adjustment. This control provides a means 
of increasing or decreasing the pull-up time. The 
adjustment changes the resistance in the first capaci¬ 
tor circuit. Increasing the resistance decreases the 
charging rate and thus deci’eases the charge which 
will be .stoi’ed in the first capacitor during the timing 
run. The adjustment is aderpiate to compensate for 
small eri-ors in sight setting and differences in the 
ballistic coefficients of different types of bombs. 
(This control is shown in simplified form in Figui’e 4 
of Chapter 2.) 

5. Torpedo tossing. In tossing torpedoes (see 
Section 2.3) the stick-length offset control is tui-ned 
to its maximum counterclockwise position, marked 
TORP. This applies a positive bias to the second 
capacitor, and consequently shortens the pirll-irp 
time sufficiently to carrse the torpedo to enter the 
water 150 to 450 ,yar-ds short of the target when the 
release altitrrde is less than 2,000 feet, and dive 
angles are between 15 and 25 degrees. The amoirnt 
the torpedo will strike short is dependent on dive 
angle and altitude of release. 

Switch Box (Transfer) 
iVIark 2, Model 1, J-108/ASG-10 

This component houses the off-on switch which 
simirltaneously connects the bomb dir-ector to the 
plane power .supply and to the bomb relea.se circirit. 
The connection is so made that the switch in its off 
positiorr retirrns the release mechanism to conven¬ 
tional electrical operation. This unit also contains a 
5-ampere circuit breaker. 

^ ^ ^ Indicator Lamp, 1MX-339/ASG-10 

This lamp lights when the .second altimeter corr- 
tact is made, indicating to the pilot that he may pull 


up; and this lamp remains lit until the bomb is 
relea.sed. A buzzer, which is wired in par-allel with 
the lamp and which pr-oduces an audible signal in 
the phone circuit, was also pr-ovided in a number of 
Model 1 computers. 

3 3 bomb director mark 1 MODEL 2, 

AN ASG-lOA 

Assembly 

The cir'cirit of the Model 2 bomb director is so 
arranged that bombs, rockets, or torpedoes can be 
to.ssed. When set for bombs, the cir-cuit is identical 
with the bomb director Mark 1 Model 1 di.scussed 
in Section 3.2. A sketch of its components is .shown 
in Figirr-e 8, and a functional diagr-am of its circuit 
in Figirre 9. Components which are rr.sed solely for 
rocket to.ssing ar-e indicated with heavy lines. The 
changes which have been made consist of adding a 
rocket calibration capacitor, a ternperatirr-e and 
lanyar-d-length control, and a relay to the compirter 
circuit, and of combining the transfer switch box 
with the contr-ol box. d'he altimeter and gyro urrits 
remain unchanged. 

Computer 

IMark 20 Alodel 2, CP-15A/ASG-10 

1. Rocket ealihration capacitor, Co. This is a 
capacitor l)ank which provides the A factor- correc¬ 
tion (.see Section 2.2.7) by reducing the capacitance 
of the secmrd charging cir-cuit at the begirrning of 
pirll-itp. It thereby .shortens the pirll-rtp time Tp, to 
compensate for the smaller tr-ajector-y dr-op in the 
case of rockets. The capacitor setting is controlled 
by the coarse rocket calibr-ation dial and is determined 
by the type of rocket to be tos.sed and the velocity 
of the plane (i.e., the A factor). The fine control, 
which corr-esjronds to the MPI adju.stment for bombs, 
is a verni3r- orr the coar-.se contr-ol. The matter of 
placing the rocket capacitor in series with the .secorrd 
capacitor- at the begirrnirrg of prrll-out is broirght 
aborrt throrrgh the action of r-elay No. 8 which is 
de-energized when the K block bob contact r-eaches 
the 1.3 segmerrt in its downwar-d motion. 

2. Temperature and lanyard-length control. The 
lar-ger trajector-y dr-op of the rockets at low ambient 
ternper-atirr-e of cold as cornpar-ed with that of r-ockets 
at high ambient temperatirre, and the dr-op which 
occurs betweerr r-elease and firing when rockets ar-e 
launched with a lanyar-d are compen.sated for by 




PRODUCTION 


35 


placing an appropriate negative charge on the Co 
capacitor prior to the beginning of pull-up. This 
has the effect of increasing the pull-up time by the 
required amount. 

3. jRelai/ No. 9. This relay serves merely to 
eliminate the effect of the rocket calibration capac¬ 
itor and relay No. 8 when the equipment is used for 
toss bombing. 


differed in a number of important mechanical design 
details. Some of the changes in the production 
models were made to facilitate their manufacture 
(see Section 3.5), others were made to improve the 
reliability of operation (see Chapter 4). The major 
difference, in the \(/ potentiometer de.sign, has been 
discussed in Chapter 2 and is di.scussed further in 
Chaj)ter G. Essentially, this change improved the 


CONTROL BOX 


TO PLANE POWER, 
BOMB RELEASE SW., 
BOMB a ROCKET 
RELEASE MECHANISM 



Figure 8. Bomb director Mark 1 Model 2, AX/ASG-lOA, components and interunit cabling. 


Control Box 

Alark 8 Model 2, C-200A ASG-10 
for Console Installation, 

C-203A ASG-10 for Surface Installation 

The control box for the Alark 1 JModel 2 contains 
the power on-off switch, test switch, gyro cage- 
uncage switch, stick-length offset, and the bomb- 
rocket transfer switch. The latter switch is set for 
whatever type of ammunition is to be used. The 
AIPI adjustment for bombs is located on the 
computer. 

^ 4 bomb director mark 1 MODEL (), 

.\N, ASG-IO(XN) 

The experimental or pilot model of the bomb 
director (Mark 1 Model 0) was essentially the same 
in principle as the two models ju.st described, but 


accuracy of the intelligence fed into the computer 
for dive angle correction and permitted satisfactory 
performance at longer ranges. 

The major mechanical design changes from the 
Model 0 were (1) improved contacts in both the 
altimeter and K lilock, (2) improved support of the 
gyro, (3) improved sealing of the computer against 
moisture and attendant electrical leakage, and 
(4) modifications in the physical dimensions of the 
equipment to facilitate installation. 

35 PRODUCTION 

3.5.1 Arrangement for Produetion 

The experimental production of bomb directoi*s 
was done largely in the development laboratories at 
Division 4’s Central Laboratories at the National 
Bureau of Standards and at the State University of 












































86 


IN STRUM ENTA HON 


Iowa (Contract No. OEAIsr-769).^^’^ Because of 
urgent I'eciuests for hoinl) directors for operational 
use, Jill appreciable number (500) of the expei-i- 
niental models (Alark 1 Alodel 0) were built. The 


(Contract No. OEMsr-1417)-°- was started before 
the experimental i)roduction program was complete. 
This meant that a number of changes in tooling and 
materials were inevitable, but it insui-ed that produc- 



only operational use (see ChajJter 4) was with 
experimental models. Also, the major installations 
at the end of the war in both Army and Navy aii- 
craft were with Model 0 bomb directors. Commeicial 
laboratories and factories furni.shed considerable 
assi.stance on the experimental production program 
largely through tlevelopment and pilot construction 
of altimeters (Contract No. OEMsr-1378)207 and of 
modified gyros (Contract No. ()EMsi-1227-°* and 
No. OEMsr-1378). 

A number of changes were made in the Model 0 
Directors during the experimental jiroduction period 
so that there were minor differences among the 500 
which were built. The nature of some of these 
differences is indicated in the following sections. 

Because of the urgency of the Service recpiests for 
the bomb directors, tooling for large-scale production 


tion facilities for an acceptable model would be 
ready at the earliest possible date. Actually the first 
production models (Model 1) became available 
about the time the last exi)erimental units (Alodel 0) 
were completed. 

The bomb director, as explained in Sections 3.2 
and 3.3, consisted of a number of distinct units 
connected by cables. A single unit was considered 
impracticable mainly because of installation and 
serviceability reciuirements. (These problems are 
discussed in Chapter 4.) Such breakdown of the 
boml) directors simplified the production program 
since various facilities could be used for the tlifferent 
components. The general plan, vhich was later 
justified by operational experience, was to build im 
excess number of altimeters and gyros for field 
rfelacement. 

























































































































rUODUCTION 


37 




Figure 11. Computer Mark 20 Model 1. with case and cover for sealed chamber removed to show accelerometer. 















38 


IIV STRUM ENTATION 


Since the essential differences in the Model 0 
and Model 1 units were in the structural design of 
the major components, the production problems will 
be presented by comprrnent headings i-ather than by 
model. The general bi'eakdown of the bomb director 
into a number of separate subassemblies further 
justifies such presentation. 

Computer 

The major prodirction problems in the computer 
wer'e (1) .sealing and drying the elements in the high- 
resistance circuits to pr-event leakage resistance from 
altering the eriuivalent resistance values, (2) design 
of the contacts in the K block to in.sur-e r-eliable 
operation over extended periods, (3) design and 
moirnting of r-elays to secrrre continuing reliable 



Figure 12. Itottonr view (with rase removed) of eom- 
])uter Mark 20 Model 1. 

operation, and (4) selection of resistors and capac¬ 
itors of proper quality and within close toler-ances 
as to value. 

1. Sealing. The capacitors Ci and To and asso¬ 
ciated chai-ging circuits, including the K block and 
connected resistors, certain critical relays, and the 


bomb release thyratron, were housed in a sealed con¬ 
tainer. Silica-gel drier was included in the container. 

The first exper-imental units u.sed a gasket sealing 
as shown in Figure 10. Later Model 0 units used 
solder sealing, but difficulties in removing the 
soldered cover for r-epair or adjustment led to a 
return to gasket sealing for production models. 

The cover for the sealed chamber in the Model 1 
was a heavy aluminum permanent-mold pressure 
casting to withstand the pressui’e changes encoun- 
tei’ed in high-altitude operation (see Figui’e 11). 
The best method of sealing the casting against small 
air leaks was an application of phenol formaldehyde 
high-temperatui’e baking enamel. This enamel did 
not lose its sealing properties when sulrjected to 
wide ranges of tempei’ature cycling. Buna S was used 
as the gasket material for Mark 1 production. 

The feed-through terminals were sealed with 
bakelite washers with neoprene bonded to both 
sides. Rubber cement was applied to the screw 
terminals before assembly. See Figure 12. 

2. Commutator. Probably the most serious defect 
of the Model 0 computer vas the shor-t-cii‘cuiting 
of the mica segments of the K block stack by metal 
particles which were ground off the brushes by 
vibration in shipment and flight. A three-leaf 
phosphor bronze brush, ir^ which the contacting 
surface was formed bv raising l^osses on the contact¬ 
ing ends, was first used to bear against the mica- 
insulated brass-segment commirtator. Initially the 
commutator svtrface was machined flat so as to leave 
the mica flush. Low insulation resistance between 
the brass segments was found to occur as an effect 
either of high humidity or of metal dust r-esirlting 
from wear of the britshes and commutator. However, 
in properly sealed comprrters the metal dirst proved 
to be the princiixil soirrce of insulation trouble. 
Undercirtting of the mica insrrlation was incorpo¬ 
rated in practically all Model 0 computers. This step 
proved helpful in eliminating this defect. It was also 
found that reirlacernent of the phosphor bronze 
bosses by either Bell No. 1 alloy or Sumet metal”“ 
as a contact metal against the brass segments 
practically eliminated wear, and thus the production 
of the metal dust which shorted out the mica insula¬ 
tion. This change was incorporated in Model 0 
computers alrout half waj' through production 
(Serial No. 2GG). 

In the Model 1 compirter the K block was built of 
0.015-in. coin .silver segments with 0.010-in. mica 
spacers. Undei’cutting, as with the later iModel 0 






















PRODUCTION 


39 


units, was tried at first but the small dimension made 
the operation very difficult. In final production the 
mica was shaped with a flat on one side of such 
dimensions as to eliminate the need for undercutting. 
The brush on the spring-supported bob was made of 
Elkonium (gold) No. 18 alloy. Extensive testing 
of the brush sliding over the commutator show'ed 
that materials became burnished w'ith use rather 
than w'orn. 

In order to reduce further the possible wear of the 
brush on the commutator, the Model 1 was provided 
with a solenoid latch for the bob. Thus the excur¬ 
sions of the bob were limited to the actual periods 
of use. 

3. Capacitors. The Model 0 units used 2-/if mica 
capacitors of selected high-insulating properties. 
Later investigations^®®^ show'ed that impregnated 
paper capacitors (Sprague Vitamin Q) could be 
obtained with excellent insulating properties. Fur- 
theimore, the 6 -/xf paper capacitor was of about the 
same size as the 2-fxi micas. Since the larger capac¬ 
itors allowed the use of smaller resistors, the special 
paper capacitors were used in the Model 1 com¬ 
puters. Capacitors were ordered w'ith plus or minus 
5 per cent tolerance and then measured and segre¬ 
gated into pairs w'ith tolerance of 2 per cent. 

4. Resistors. Precision wire-wound resistoi*s on 
ceramic forms (see Figure 6 ) were used in the capac¬ 
itor-charging circuits. It was essential that the 
resistors be stable under wide temperature and 
humidity cycles and also under severe vibration. 
It was found that some of the resistors developed 
open circuits under vibration. The defective units 
were eliminated by requiring all resistors to pass a 
vibration test. 

In the Model 0 computers the resistors used were 
obtained from the single manufacturer w'hose product 
stood up w'ell under temperature cycling and humid¬ 
ity tests.®®®’®^®’^®^ In the case of the Model 1 equip¬ 
ment, it was necessary to have several sources of 
resistors, and it w'as found necessary by the produc¬ 
tion company to temperature-cycle all resistors for 
four cycles, and to sort out for use only those re¬ 
sistors which did not change excessively in resistance. 
Resistance values were measured to within 0.1 per 
cent and those w'hich changed more than 0.5 per cent 
after cycling w'ere discarded. This procedure insured 
reliable components but required extensive resistor 
testing (several thousand measurements per day) 
for the estimated production rate of 1,000 computers 
per month. 


Final exact adjustment of the RC ratio of the two 
charging circuits was made in a 20,(XX)-ohm poten¬ 
tiometer shown l)elow the MPI adjustment in 
Figure 2 . 

5. Relays. No relays w'ere available commercially 
with adequate current carrying capacity and leakage 
resistance, small enough w'eight, short enough 
operating time.^®® The Magnavox Company, in 
cooperation with the North Electric Company, 
developed a special relay for the computer. Current 
capacity of 10 amperes and an operating time of 
less than 0.012 second w'ere required. 

6 . Thyratron. The thyratrons in computer circuits 
were the 2050 type specially selected for high grid 
impedance.®®’®®^®® It was also necessary to select 
thyratrons for the altimeter control circuit with 
deionization times of less than a millisecond. 

7. Accelerometer. The material selected for the 
spring in the accelerometer w'as an alloy known 
commercially as Iso-elastic. It consisted of 36 per 
cent Ni, 8 per cent Cr, 0.5 per cent Mo, and the 
balance Fe.‘^®® 

In the Model 0 units the w'eights w'ere adjusted 
individually to match the springs. In the Model 1 
units all the weights were the same and an arrange¬ 
ment was devised to adjust the spring constant and 
the spring position. These tw'o independent adjust¬ 
ments permitted a straightforw'ard assembly and 
testing technique for production. 

Gyro 

The gju-o component of the tossing equipment w'as 
a Sperry Artificial Horizon Gyroscope modified to 
slide a contact over a potentiometer. This operation 
fed to the computer a voltage which w'as a function 
of the angle of dive. The production of this com¬ 
ponent disclosed a number of problems, particularly 
in the design and adju.stment of the contacting 
element, in proper shock mounting, in securing a 
simple and reliable caging mechanism, and in insur¬ 
ing tha t the necessaiy alterations to the gyro did not 

impair its reliability in operation. 137 b 

describe the gyro problems in detail. Thej'’ will be 
summarized briefly here. 

\}/ Card Potentiometer. The first experimental 
1 /' card W'as w'ound on a simple rectangle of bakelite. 
The Model 0 and Model 1 cards consisted of a 
three-step sheet; and the former is pictured in 
Figure 5. They are further described in Section G.3.3. 
Various methods w'ere developed for winding, shap- 







40 


INSTRUMENTATION 


ing, and installing the card in the potentiometer. 
The first models employed an aluminum envelope or 
card holder which held the resistance card. Th.e 
latter was wound on a straight piece of bakelite and 
then flexed so that it could be forced into the pocket 
of the card holder. The aluminum card holder was 
shaped to a definite radius of curvature. It was soon 
found desirable to eliminate the aluminum cjird 
holder, and use a heat-formed card provided with 
metal end fittings for attachment to the gyro case. 
A more satisfactory production technicpie was 
established by using a special, paitially cured plastic 
material. Suitable hard-drawn Advance wire was 
w’ound on a straight card which was subseciuently 
heat-formed to the proper radius and cured in this 
shape. The necessary adjustment for correct angular 
positioning of the card was i)i-ovided by using slotted 
holes in the case. These were sealed against air 
leakage b\ using external rubbei- washers. A further 
improvement in late Model 0 units (subsequent to 
serial numbei- 525 and designated as AN, ASG-XN2) 
was secured b\ devising a molded bakelite card 
holder provided with metal inserts for the attach¬ 
ment sci-ews. Also, a potentiometer card approx- 



Figurk 13. Interior view of ^:vro .Mark 20 Model 0 
(XN2), showdng ixReiVionietei’ card (at right) and con¬ 
tact arm. 

imating the Model 1 card was used. This type of 
construction insured high electrical insulation re¬ 
sistance to the case and held the card to a fixed 
radius of curvature, while the molded holder insured 


that the card wmuld not warp to such an extent that 
the pointer might mjt make contact. 

The Model 1 units wei-e J)ro^■ided with a cam 
adjustment foi lo(*ating the card in its correct 
angular position. Metal end fittings wei-e used for 
clamping the card in its final j^osition after- it was 
irropei’ly h'cated. Slots to per-rnit adjustment of the 
card wer-e located in the card end fittings rather than 
in the case, as w as done in the ear-ly Model 0 units. 

The techniciue of winding and cleaning the con¬ 
tacting edge portion of the card was consider-ably 
improved during j)ilot prr'duction and the final 
pr-oductiqn irnits show'ed greatly impr'oved per¬ 
formance. Gyr-o units wei’e only considei-ed accept- 
able if the continuity of contact along the contact¬ 
ing edge of the car’d showed very small var-iations 
when tested wdth a low-voltage olirnrnetei-. Pi-operly 
cleaned car-ds wer-e found to maintain this condition 
over an extended period of time. An interior view 
of a modified gyro showing the jjotentiometer card, 
contacting arm, and leads is given in Figure 13. 

Contact arm rlifficulties with ear-ly pilot models 
disclosed that the contact finger was poorly balanced. 
Vibration of the gyro caused the silver V-shaped 
contact to hammer on the potentiometer until it 
cut through the r esistance wir-e of the str-ip. Smaller 



FiGi Rr: 14. Components of gyro contact arm. (Assem¬ 
bled contact arm shown at right.) 

contact points anil better- balanced assemblies 
eliminated the difficulty. 

In production models the contact finger w'as 
firrther- modified to allow- exact assembly on a 
production-line ba.sis. Provision was made to permit 
a bending of the contact finger for good contact 
without affecting clear-ances. Bell No. 1 gold alloy 





PRODUCTION 


41 


\vas substituted ter silvei- as a contact material. 
Details of the contact elements are shown in Figure 
14 and the method of asseml)ling the contact arm 
on the gimhal ring of the gyro is shown in Figure 15. 



Figi’rk 1,0. (lyro witli ca^e removed, showing!; i)eii- 
diilous housing, fiimhal ritifi and contact arm. 

It was felt that the simple interchangeability of 
resistance card as.sembly proeided in the Model 0 
design should have been retained in the production 
design. However, considerable progress had been 
made in the manufacture of tools for the production 
model befoie the last Model 0 design was completed. 
Later it was found e.xpedient to incorporate certain 
of the features of the later ]\Iodel 0 design in the 
Model 1. 

Early models of the gyros developed defects due 
to air leakage at the point where the electrical leads 
were brought through the case. The later Model 0 
design included a lead-through in the form of a rubber 
button molded around the insulated wires. This 
insulating button was clamped against the case to 
minimize air leakage. The Model 1 design employed 


a molded bakelite lead-through w'ith through metal 
inserts to w'hich the wires w'ere soldered. This lead- 
through w'as clamped to the case and cemented. 

Caging. The first few Model 0 units w'ere equipped 
for manual caging of the gyroscope. A flexible drive 
a few feet long permitted mounting the gyro at a 
convenient distance from the pilot’s control panel, 
at the same time permitting the caging knob to be 
located w’here it would be accessible to the pilot in 
flight. How'ever, the flexible drive shaft could not be 
removed easily and its installation, adjustment, and 
removal from the plane proved to be quite trouble- 
.some. An electrical caging mechanism, consisting 
of a 28-volt series motor with a gear box and suitable 
limit switches was designed and incorporated in an 
improved type of shock mounting for the gyro. 
This new arrangement permitted caging and uncag¬ 
ing the gyro by the flip of a switch as compared with 
a pull, tw'ist, and locking into jiosition of the earlier 
manual caging knob. 

The caging mechanism consisted, in part, of a 
series motor which had two field windings wound in 
opposite directions. One side of the armature was 
grounded and the other side connected to one end of 
each field winding. By connecting the live side of 
the grounded power source to the free end of one 
or the other field winding, either direction of rota¬ 
tion was obtained. Limit switches were provided in 
series with each field winding. These limit switches 
were operated by a cam in the gear box. One was 
adjusted to insure that the circuit would be opened 
when the gyro was uncaged to such an extent that 
the caging dogs would not interfere with the gyro 
within its normal oj)erating limits. The other limit 
switch was adjusted to open when the gyro was 
caged. The wind-up toixpie on the drive spring was 
sufficient to keep the gyro caged. 

Trouble was experienced with some of the first 
electrical caging motors because of excessive speeds 
in caging and uncaging. It was found expedient to 
c(jrrect any trouble arising from motors giving 
excessive speeds, by .shunting the armature with a 
fixed resistor of approximately 15 ohms. This shunt 
insured that the starting torque w'ould not be greatly 
reduced, and at the same time limited the maximum 
speed of the caging motor at the expense of a slight 
increa.se in pow'er requirements. The shunt method 
was used in the Model 1 units. 

An alternative speed reducing technique, incor¬ 
porated in the later Model 0 units, consi.sted of a 
solenoid-operated brake. This was superior to the 




42 


IN STRUM ENTATION 


shunt method in that over-travel of motors could he 
reduced to a minimum. Because of the urgency of 
the program, it was not feasible to redesign the motor 
and incorporate a brake; so for expediency, a brake 
tearing on the armature was added to the available 
motor. 

Tests of some of the first mechanisms at low 
temperature ( —40C) revealed eriatic performance 


Shock Mounting. Best operation of the contacts 
in the potentiometer in the gyro reciuired that vibra¬ 
tion induced by the aircraft be minimized. In addi¬ 
tion, the gimbal bearings in the gyro were susceptible 
to shock so insulation of the equipment from shock 
was important. Changing from manual to electrical 
caging simplified the problem of insulating the gyro 
from external disturbances. 



Figure 10. Components of gyro Mark 20 Model 1 (Magnavox drawing). 


due to large variations in the torcjue recpiired to cage 
and uncage different gyros. This led to specification 
of tolerances for the caging torque which when 
followed insured a more uniform production and 
satisfactory operation of the caging mechanism at 
low temperatures. 


^"alious shock mounting systems were tried l^oth 
in the pilot and final production. It jtroved necessary 
to incorporate a snubbing action in order to limit 
excursion under extreme shock. 

The Model 0 design of shock mounting for the 
gyro consisted essentially of a framework which 


































PRODUCTION 


43 


carried four Lord buttons, two located in front and 
below the gyro and two above at the rear of the 
gyro. The design of this mount insured that the 
center of gravity of the modified gyro was located 
in the plane of the four buttons. Buttons of 1-pound 
rating were used, although 2-pound buttons, which 
were not available, were preferred. 

The Model 1 design used 2-pound buttons, which 
had become obtainable. The final design used two 
of these buttons in tandem at each point of support. 
The location of these buttons may be seen on the 
mounting fi-ame and front support in Figui-e 16. 
This figure illustrates the general arrangement of the 
Mark 1 gyro-mounting system. 

Some difficulty was experienced from bearing 
failures in the gyro dui-ing shipment. This appar¬ 
ently vas due to bending of the frame lug which 
carried the gimbal assembly, part of which had been 
milled away to accommodate the changes made to 
the gyro. An improved, cushioned package for 
shipping the gyros eliminated the failures. 

In order to reduce the possibility that the vibration 
of the potentiometer contact would cause voltage 
fluctuations during operations, a 0.5-/xf capacitor 
was added between the pointer and ground (see 
Figure 2). A further precaution was a 330,000-ohm 
resistor by-passing the potentiometer, to provide 
charging voltage in case of an open circuit in the 
potentiometer. This provided a charging voltage 
corresponding to a 40-degree dive. Although this 
precaution appeared desirable on very early models, 
it was probabl}^ superfluous on the production 
models. 

Banking Limitation. The original design of the 
caging mechanism was such that in the uncaged 
condition a roll of 70 degrees would disturb the inner 
gimbal (spill the gyro). This imposed a serious 
tactical limitation on the use of the bomb director 
since common dive bombing tactics call for a sharp 
turn prior to the dive, with a bank of about 80 de¬ 
grees or more. (To avoid disturbing the gyro, pilots 
had been using a push-over type of entry into the 
dive.) 

A number of simple modifications devised to 
remove this limitation were put into production 
toward the end of the program.These changes 
were: (1) Removing the bumper on the bottom of the 
pendulous housing; (2) sliding a piece of rubber 
tubing over the caging arm; (3) installing on the 
gimbal ring a metal plate with tabs turned up at 
right angles (this plate, in conjunction with the 


rubber tubing, acts as a stop); (4) careful filing of the 
supporting fin on the inside of the gimbal ring to 
allow clearance for one pendulous vane; (5) adjust¬ 
ing the new stops and rebalancing the gyro. 

Gyros so modified successfully underwent flight 
tests in which the pilot made (a) 85-degree banks, 

(b) 85-degree banks followed by 90-degree turns, 

(c) 85-degree to 90-degree banks simultaneously 
with 50- to 55-degree dives and 90-degree turns. In 
no case was the gyro spilled. 

In view of this performance and of the fact that 
the required changes were of such a nature that they 
could easily be made in the field, a program of this 
conversion was begun in August 1945. 

Altimeter Unit 

The first altimeter units were 50,000-foot sensitive 
Kollsman altimeters which were modified by the 
addition of electrical contacts in the laboratory. 
Considerable effort was spent in devising a delicate 
contact which would not seriously affect the altitude 
indication of the altimeter.^®* A number of models 
were made before the contact mechanism was 
finally considered adequate. It was found desirable 
to use a gold alloy “whisker” 1 inch long with its 
inner end mounted on and electrically connected 
to the 1,000-foot pointer, which was grounded through 
the gear mechanism of the instrument. In order to 
increase the initial contact force of this fine whisker 
on the altitude prongs, the whisker, 0.01 inch wide 
by 0.001 inch thick, was threaded through a small 
loop projecting beyond the end of the pointer to 
within 0.1 inch of the end of the whisker (see Figure 
3). This loop acted as a fulcrum so that when the 
tip of the whisker came in contact with the prong 
the contact force was initially fairly high and re¬ 
mained high until the contact was broken. It was 
important that the whisker have sufficient initial 
set to make it press against the trailing edge of the 
loop, even when free of the prong. Approximately 
constant pressure was insured by this design so that 
with properly cleaned platinum or gold alloy prongs 
the “continuity of contact” was good for the com¬ 
plete duration of contact. In order to reduce burn¬ 
ing of the tip of the whisker, a 500-ohm resistoi- was 
connected in series with the prong ring to limit the 
current flowing through the tip of the whisker as a 
result of discharge of the capacitor when the circuit 
was broken. 








44 


INSTRUM EN TA TION 


Twelve wedge-shaped noble metal prongs were 
placed at altitude points around the periphery as 
shown in Figure 3. The prongs were supported and 
electrically connected by a brass ring. The pressure 
exerted by the gold whisker on the wedge-shaped 
prongs was so low that it was found necessary to 
take great care in cleaning the metal prongs. The 
most satisfactory method evolved for cleaning the 
prongs consisted in a final operation of removing 
metal by scraping or filing along the contact edge. 
For this reason plated prongs did not prove satis¬ 
factory. Other attempts at cleaning chemically, 
by metallographic paper, etc., did not always leave 
an adeciuately clean contact surface. 

In order to minimize “first button release” trouble 
which might be the result of intermittent contact 
between the whisker and the prong, a circuit having 
a time constant of Yi second was introduced between 


molding. The bakelite ring incorporated an elec¬ 
trical lead-through to permit external connections 
and at the same time an airtight seal of the altimeter. 
The prongs were threaded through holes in the brass 
ring and soft-soldered to it. The prongs were shaped 
in such a way that they could be bent so as to permit 
adjustment to the precise altitude positions desired. 
The insulation material in the late Model 0 units 
was BM 14726. After curing at 300 F for three 
hours the ring assembly would withstand repeated 
temperature cycling between the limits —60 and 
-f65 C without cracking. The design of the Model 1 
incorporated straight prongs placed in the prong 
ring and subsequently swaged to have a wedge 
shape toward the contacting edge. 

The design of the contacting mechanism in the 
altimeter unit was such that the altimeter indications 
were not appreciably affected; except that it was 



the prong ring and the grid of the thyratron to 
which it was connected. This circuit consisted of a 
3 < 4 -Mf capacitor shunted ]\v a 2-megohm resistoi- 
(.see Figure 2). 

Simple electrical insulation of the prong ring b}" 
means of varnished caml)ric and varnished glass 
cloth proved inadeciuate under high humidity condi¬ 
tions. In fact, the introduction of the time delay 
element having the capacitor and 2-megohm resistor 
retpiired that the insulation resistance between the 
altimeter prong ring and ground be at least three 
megohms. Several designs of bakelite molded prong 
rings were tried before a satisfactory one was 
evolved. Better insulation was secured by molding 
the ring and its prongs as an insert in the bakelite 


necessary to adjust the altimeter to indicate zero 
at the target, the altimeter unit was availal)le in 
use as a flight instrument. In the experimental 
models it was found convenient to mount the alti¬ 
meter in the panel in the bombardier’s cockpit and 
therel:)y make use of the shock mounting already 
provided in the panel. However, the very lightweight 
design of the contact mechanism incorporated in the 
altimeter made it desirable to provide even better 
.shock mounting for the altimeter than that provided 
for the instrument panel. The best procedure 
seemed to be installation of the altimeter unit on a 
specially isolated instrument panel. 

The general assembly layout of the Model 1 
altimeter is shown in Figure 17. 




































LABOR A rO R\ 1KS11N <; 


45 


^ LABORATORY TESTING 

Objective 

In view of the experimental nature of the produc¬ 
tion of the bomb director IMark 1 Model 0 and the 
initial 500 Mark 1 Model 1 equipment, it was con¬ 
sidered advisable to inspect and test all major 
components individually before issue to the Services. 
Accordingly, Division 4 carried on, at its central 
laboratories at the National Bureau of Standards, 
acceptance type tests on all Model 0 units and 
Model 1 units up until the time the project was 
turned over to the Navy. 

An attempt was made wherever possible to apply 
overall functional tests to the equipment, rather 
than to check individual parts. The inspection 
proved to be of definite value in uncovering defects 
in factory inspection and in design. 

The details of testing equipment procedures and 
acceptance limits are given in the following sections. 
While the exact limits and certain details of pro¬ 
cedure varied during the course of the program, the 
summary given here represents the final require¬ 
ments. 

The final specifications given in reference 138 are 
based on experience gained in acceptance testing 
of the Alodel 0 and the initial 500 Model 1 equip¬ 
ment. 


Computer 

1 . Features tested. The computer was put through 
a series of overall performance cycles while placed 



Figure 18. Block diagram of centrifuge test set to 
check operation of computers under acceleration. 


in a centrifuge oriented with re.spect to the accelera¬ 
tion as it would be in .service. No gyro was connected. 


The computer was tested at rest and under eight 
different values of acceleration. The output time 
was measured in each case for a 2-second input. 

2. Equipment. The testing equipment consisted 
of the following principal components arranged 
schematically as .<?hown in Figure 18 and in photo¬ 
graphs, Figures 19 and 20. (a) Centrifuge arranged 



Figure 19. Photograph of centrifuge sliovving com- 
{luter mounted on one arm of centrifuge. Note 11 
brushes and slip rings at top left for bringing test leads 
to two computers. Lowest spring on brush block is con¬ 
tact for cam used for two computers; right-hand timer 
times 10 revolutions of computer. 

to carry two computers and rotate them to obtain 
accelerations similar to Service conditions. (Ii) A 
1 -hp d-c motor to drive the centrifuge through a 
20 to 1 reduction gear box. (c) A tachometer of 
permanent magnet type which gat’e a voltage pro¬ 
portional to speed. Its armature was fastened to 
the motor .shaft, (d) The GE tachometer signal 
Thymotrol was a thyratron system of current control 
in which the motor was brought up to a speed such 
that the voltage output of the tachometer generator 
balanced a network involving a set of voltage regu¬ 
lator tubes, a d-c amplifier, and a pair of adjustable 
wire-wound resistors. These resistors served as 
adjustments of the centrifuge running speed. One 
.served as a coarse and the other as a fine adjustment. 
An eight-point switch served to cut in any one of 
eight pairs of such resistors. Each pair of resistors 
was adjusted to give one arbitrary centrifuge speed. 
It was then nece.s.sarv only to turn the multiple 
point switch to get any one of the eight standard 























46 


IN STRUM ENTATION 


running speeds. Once the system was wanned up 
for an liour the speed remained constant to about 
0.2 per cent, (e) A computer test set to put time 
into both computers simultaneously and to measure 
output time with one timer for each computer. This 
circuit was essentially similar to that described in 



Figure 20. (’ontrol panel for Thyinotrol. Lower 
section contains timers for two comiinters; right-liand 
timer times 10 revolutions of centrifuge. 

reference 65. (f) A revolution timer which measured 
the time for ten revolutions of the centrifuge. This 
was operated Ity a cam, mounted on the .shaft, which 
closed a circuit which actuated a rotating switch at 
each revolution. This relay energized the timer 
clutch during the time interval of the ten revolutions. 

3. Acceptance limits. The units were checked at 
rest with .supply of 24, 27, and 30 volts. Accuracy 
of plus or minus 1 per cent of theoretical values was 
required. The unit was required to operate, without 
regard to accuracy, with a 20-volt supply. With the 
centrifuge in motion the unit was te.^^ted at eight 


particular speeds corresponding to values of acceler¬ 
ation approximately equally spaced between 1.41(7 
and 5.77g. The acceptance limits at each speed 
allowed an error of plus or minus 1 per cent due to 
resistance values in the charging circuits and an 
error due to the K block making contact with the 
segment adjacent to the theoretically correct one. 

The value of rotational speed required for any 
given K value was calculated from the equation 

K = 

9 

where K is the acceleration in g units, R is the radius 
to the center of gravity of the K block, N is the 
number of revolutions per second, and g the acceler¬ 
ation of gravity. 

The acceptance time limits were rounded off to 
multiples of 0.01 second in order to widen the limits. 

Less than 5 per cent of the Model 1 computers 
failed to pass the centrifuge te.st. 

.V6..I 

The g 3 'ro unit was an item of .such a nature that 
defects in manufacture were very likely to slip by 
undetected. Tests were made as follows: 

1. A caging test to insure that: (a) Both caging 
and uncaging operations took less than five seconds 
at 28 volts. (Ij) The operations were satisfactory 
with a 20-volt supply, (c) When uncaging, the 
caging dogs did not strike the stops, (d) When 
caging, the overtravel of the motor should be about 
90 degrees to pro^•ide proper tension to keep the 
gyro caged, (e) The limit switches on the caging 
motor operated posit ivety at each end of the motor 
stroke. This was done with an ammeter in the 
caging circuit, (f) The gyro was caged in the 45- 
degree climb position to insure that the coupling 
spring did not snap out of place. With the gyro in 
the climb position the spring suffered its maximum 
elongation. In some cases, where the clearance was 
excessive, the spring was found to jump out of place. 

2 . A check to insure that the contactor made 
contact with the resistance card at all points and 
that the pointer, if energized either at a climb angle 
or a div'e angle of over 75 degrees, would ride pioperly 
onto the card. The solenoid was expected to operate 
the pointer on a 20-volt .supply. 

3. Contact continuity. Failure to obtain electrical 
continuity between the pointer and the resistance 











LA HOK ATOR Y I P:STING 


47 


card was the most frecjiient source of rejection. A 
tilt table, provided with a coarse worm gear drive, 
w’as used tor this test. The gyro w'as leveled and the 
solenoid energized. An electronic ohmmeter was 
then used to measure the resistance between the 
leads. As the gyro was tilted slowly, the resistance 
was recjuired to change continuously. If at any 
point the resistance jumped up to infinity the gyro 
was rejected. The contact continuity was checked 
with the gyro tilted first slowly in the di\'e direction, 
then back to the level position. 

4. Precession test. In order to insure that the gyro 
would not process excessively due either to high 
contact pressure or to a rough card, the pointer was 
energized with the gyro leveled. The gyro was then 
tilted slow'ly and uniformly to the 75-degree dive 
position in one minute. The gyro woidd then process 
in the roll direction. The solenoid was then de¬ 
energized, the gyro brought back quickly to the 
horizontal position and rotated through 90 degrees 
about a vertical axis. The roll precession was then 
transferred to the pointer and was read directly on 
the glass scale. The acceptable limit for this pre¬ 
cession was 23 degrees. 

5. Voltage distribution. The distribution of voltage 
over the potentiometer card was measured-® in a 
.“^etup arranged to .show directly in volts the depar¬ 
ture from the nominal resistance. Tolei-ances were as 
follows: 


Fractions of the Total Voltage 


Aii-rle 

Fraction 

Toler.ance 

0-10° 

1.00 

l.ov 

14.6 

0.960 

1.0 

21.9 

0.896 

1.0 

.31.2 

0.814 

1.0 

40.6 

0.712 

1.0 

.■)0.6 

0.592 

1.5 

60.4 

0.4.587 

2.0 


The test set was originally designed for the 
Model 0 XN-1 gyro card which gave the al)ove 
voltages at angles of even multiples of 10 degrees. 
However, when the XN-2 and the Model 1 gyros 
were tested, the voltage values were retained, but 
the angles were changed slightly to conform to the 
new card design. 

(). Voltage proof test. This test measured the 
insulation resistance between the pointer and ca.se, 
both with and without the solenoid energized. A 
t-est was also made of the resistance between the 


strip and case. The loudest acceptable value was 
200 megohms in an atmosphere of 60 per cent rela¬ 
tive humidity. 

Altimeter Unit 

The most critical features of the altimeter unit 
were the duration of contact, the continuity of 
contact, and the accuracy of the altitude at which 
each contact w^as made. The.se features w'ere 
checked as w'ell as electrical leakage resistance from 
the contact ring to case, air leakage of the ca.se, and 
the so-called po.sition error, i.e., the shift in reading 
due to changing orientation of the instrument. 

The particular tests follow: 

Calibration. The calibration was performed in 
tw’o stages. First, the indicated altitude was read 
at the instant that contact was made, i.e., the read¬ 
ing of the altimeter itself was taken without regard 
to its ow'n instrumental correction, llie second 
stage consisted of placing the instrument in a low- 
pressure chamber and checking the instrumental 
error, or the pressure at which each contact was 
made. 

1 . The indicated reading was determined as 
follows: The altimeter was adjusted by turning the 
adjustment knob until the reading was w'ell over 
10,328 feet. 

The adjustment knob was then rotated so that 
the instrument read decreasing altitude. The point 
of contact was then indicated by an ohmmeter. As 
the wdiisker made contact with each prong in suc¬ 
cession, the indicated altitude w-as read. These 
readings were recpiired to agree with the theoretical 
altitude within 15 feet. 

2. The second stage of calibration w’as done by 
placing the altimeter in a steel low'-pres.sure chamber. 
A \ ibrator was mounted on the rack which held the 
instrument. Its ])urpo.se was to shake out most of the 
friction in the altimeter mechanisms. The chamber 
held six altimeters simultaneously. 

A pair of leads was brought out of the chamber 
from each instrument. By means of a multiple- 
point switch each one in turn was connected with a 
computer so modified that a relay operated and a 
neon light flashed each time the whisker made 
contact with a prong. 

The chamber was evacuated five times to the 
pressure equivalent of 20,000 feet and then brought 
back slowly to atmosphei'ic pressure. The purpose 










48 


IN S IK U.M ENT ATION 


of the five pressure cycles was to get the instruments 
into a standard condition with respect to hysteresis. 

The pressure of the chamber was read Avith an 
unmodified Kollsman altimeter which was period¬ 
ically checked by the Aeronautical Instruments 
Section of the National Bureau of Standards. 

A reading was made of the standard altimeter 
each time the test altimeter made contact. 

The instrumental error, the theoretical altitude 
minus the indicated altitude, was kept within limits 
as specified in Joint Army-Navy Specification 
AN GG 461, except that when the error was appre¬ 
ciable at the low altitudes, the zero was shifted to 
reduce all values by a constant amount. 

The calibration of the altimeter unit IMark 1 
Model 1 was adju.sted by the manufacturer so that 
the altimeter scale error was as small as possible 
over the range 0 to 16,000 feet. It had been hoped 
that by doing so and by making slight compensation 
for the scale error in locating the contact pins, a 
higher order of accuracy could be obtained. How¬ 
ever, difficulties in absolute calibration raised serious 
questions as to the advisability of making pin 
adjustments to compensate for scale error. 

Contact Duration and Continuity. Along with the 
first part of the calibration test a reading was taken 
of the altitude at which contact was broken. The 
difference between the “break” and the “make” 
points was required to be between 40 and 60 feet 
for the altitudes 1,390 to 2,402 feet, and between 
40 and 75 feet for the points 2,882 to 10,328. 

Over the range lietween the make and the break, 
continuous low-resistance contact was required. 
Unless the contact pins were properly shaped and 
scraped, and the proper whisker design and tension 
maintained, the whisker could make mechanical 
contact while the resistance between elements would 
be of the order of several hundred megohms. 

Air Leakage. The instrument case was connected 
to a vacuum line and exhausted to 1,000 feet. The 
vacuum connection was then closed. If air leaked 
into the case fast enough to drop the reading by 


100 feet per minute, the instrument was rejected. 

Insulation Resistance. The resistance between the 
contact ring and the case was measured as a function 
of ambient humidity. The tolerance limits follow: 


Relative humidity 

Lower limit 

per cent 

megohms 

30 

10,000 

40 

4,000 

50 

2,000 

60 

600 

70 

300 

80 

120 

90 

50 

95 

30 

Position Error. The instrument was placed with 
its face in a vertical plane and adjusted to an integral 

multiple of 1,000-foot reading, 

with the 100-foot 

hand vertical. The instrument 

was then tapped 


gently by the operator until the 100-foot hand 
settled at one point. The operation of tapping was 
twice repeated rotating the instrument first 120 
degrees, then 240 degrees about its axis. If the 
maximum difference between any two readings 
exceeded 20 feet, the altimeter was rejected. 

This test was repeated for two other altitudes of 
about 250 and 500 feet greater than the first. 

Control Box 

This control box was inspected in a special test 
set which checked continuity of each circuit and the 
approximate values of the !\1PI and stick-offset 
resistors. The acceptable limits were approximate!}' 
plus or minus 10 per cent of the nominal value of the 
resistance at each indicated point. At the three 
lowest resistance values the correct resistance was 
to be obtained with the pointer set within one divi¬ 
sion of the correct one. 

The control box Mark 8 Model 1 was not checked 
as an acceptance control since the production inspec¬ 
tion was considered satisfactory. 


KKSTRICTKl) 










Chapter 1 

INSTALLATION, OPERATION, AND MAINTENANCE 


I X THE FOLLOWING PARAGKAPHS a picture of the 
general problem of installation is given, with a 
rather more detailed discussion of the flight tests 
required following installation. 

Published information, such as installation 

and operating manuals,270.272-274 

gives a still greater detailed description of the prob- 


l\STALLATI()\ 

^ ' ' Computer 

The computer is so installed that the enclosed 
accelerometer measures the component of spatial 
acceleration perpendicular to the flight line. This is 



Figtre 1. Bomb director .Mark 1 .Model 1 eomponent.s, minus interunit eai)Iinf;:- 


lems. A photograph of the items to be installed, 
less connecting cables, is .shown in Figure 1. Place¬ 
ment of the components in typical Navy planes is 
shown in Figure 2. 

^This etiapter \va.s written by P. V. Johason of the National 
Bureau of Standard.s. 


accomplished when the ba.se of the unit is in a 
geometrical plane that is parallel with the flight line 
and the line joining the wing tips, i.e., its base is level 
during level flight. Whether the computer is posi¬ 
tioned lengthwise or athwartship does not affect 
its operation. It is preferable, but not imperative. 


49 






50 


INSTALLATION, OPERATION, AND MAINTENANCE 


that the computer be near the center of gravity of 
the airplane. 

Gyro 

The gyro is located within 9 feet of the center of 
gravity of the airplane, and positioned athwartship 
vith its glass face plate facing to starboard (right). 
Vacuum line and electrical connections are so made 


plane in an average or typical dive under operational 
speeds or loads. A vacuum of 4 i 34 i^^h of mercury 
is required for proper operation. 

Altimeter 

The altimeter is variously installed as a replace¬ 
ment for the regular flight instrument or as a separate 



Figure 2. Placement of bomb director eciniimient in 3 Navy aircraft (U. S. Xavj" drawing). 


that no interference with free movement of the gyro 
in its shock mounting is cau.sed. It is of prime im¬ 
portance that the gyro lie so leveled that the indi¬ 
cated zero angle is that of the flight line of the air- 


flight instrument in single-place airplanes and as a 
replacement for the bombardier’s altimeter in two 
place aircraft. It is positioned so as to be readily 
accessible to the pilot (or bombardier) for adjust- 





















































EXPERIMENTAL FLIGHT TEST PROCEDURES 


ment. Special care is taken to insure that there is no 
restriction to free movement on its shock mount. 

* ‘ ^ Control Boxes 

The pilot’s control box is either surface mounted 
or is mounted as part of a console installation. No 
particular requirements are to be met other than 
accessibility to either the pilot or bombardier. 

The transfer switch box is generally located so as 
to be readily accessible to the pilot in all types of 
airplanes. 

Indicator Lamp 

The indicator lamp is mounted near the pilot’s 
gunsight and aligned ^\ith the pilot’s eye during 
glide bombing so that the light may be observed 
V ithout shifting attention from the sight. 

Gunsight 

Any standard-type gunsight is satisfactory^^- 
provided due consideration is given to the problem 
of alignment so that the sight line and flight line 
coincide in a dive under median conditions of dive 
angle, airspeed, and loading. This subject is treated 
in Section 4.2.1. 

^ 2 EXPERIMENTAL FLIGHT TEST 
PROCEDURES 

* Calibration Tests 

for Toss Bombing 

Normal procedure in alignment'^ of the gunsight 
in airplanes such as are used in toss bombing calls 
for the sight line to be adjusted for use in gunnery. 
Since conditions considered as median for gunneiy 
are quite different from those for toss bombing, a 
problem of proper sight alignment is presented. For 
gunneiy, the sight and guns are harmonized for 
flight conditions encountered in level flight and at 
considerably lower speeds than those used in toss 
bombing; the difference in angle of attack may be as 
much as 40 mils in the two techniques. 

If a gunsight with a fixed reflector plate is used, 
its suitability for either gunnery or toss bombing 
can be accomplished by use of a reticle modified to 
contain two pips so positioned that when the plane 

^ The importance of sight alignment and angle of attack 
variations is discussed later in Section 6.4.11. 


is boresighted for gunnery using the central pip, the 
other then becomes the sighting line for median toss 
bombing conditions. Median conditions are usually 
considered as 400 mph in a 40-degree dive. If a 
gunsight with an adjustable reflector is available, 
it is obvious that a mere turn of the adjusting knob 
will properly align the sight for whichever use is 
desired. 

The primary problem, then, is one of determining 
the proper alignment to insure coincidence of the 
sight line and flight line for each plane or an average 
setting for all planes of one type. There can be 
considerable variation in the angle of attack of a 
number of planes even of one type, which may, in 
part, account for the difficulty encountered in using 
engineering data supplied by manufacturers, or 
found in aircraft manuals, to determine accurate!}' 
the difference between sight and flight lines. Some 
published data, such as those in reference 214, proved 
fairly reliable and usefid for some plane types, but 
unsuitable for other types when used in toss bomb¬ 
ing. Thus, it is deemed advisable to calibrate each 
airplane following installation of toss bombing 
equipment. 

Two methods of calibration in flight have been 
used, both of which appear to be satisfactory. In 
one, a stationary theodolite is used as an aiming 
point toward which a plane dives. An arbitrary 
sight setting is previously made from engineering 
data or past experience, the plane is loaded with an 
average combat load, and a dive is made using pre¬ 
determined dive angle and airspeed corresponding to 
av'erage toss bombing conditions. If the sight is 
properly set, an observer at the theodolite determines 
when the plane is flying a straight course relative 
to the cross hairs toward the target. If the flight 
path is not straight, but the plane appears to rise 
or fall, this information is transmitted to the pilot 
and the sight raised or lowered for subsequent dives. 
A number of such dives are necessary from headings 
180 degrees apart; the average of the two sight set¬ 
tings, one for each heading, is taken as a no-wind 
value. Accurate determinations by this method are 
difficult and probably unsatisfactory if made under 
conditions where the wind exceeds 10 knots. 

The other method consists of dropping bombs and 
adjusting the sight setting until the no-wind MPI 
with respect to the point of aim is within desired 
limits. Calibration flights in naval stations and 
army fields for tests mentioned in this volume were 
done using median conditions of dive angle, altitude. 




52 


INSTALLA JION, OPERATION, AND MAINTENANCE 


airspeed, and plane loading. Sight settings thus 
obtained were found satisfactory. In calibrating 
P-47 aircraft of the Ninth Air Force in the European 
Theater of Operations [ETO], however, it was found 
more desirable to calibrate the sight at low altitudes 
(two lowest altimeter contacts), low dive angles 
(15-20 degrees) and indicated airspeeds [IAS] of 
about 350 mph. Since impact errors aix* grc-atc'st 
under these conditions, .sharper adjustment to the 
sight setting could be made, and fewer bombs were 
recpiired to complete the calibration. 

Since wind errors must be eliminated from cali¬ 
bration results, it is desirable that runs be made on 
dead crosswind headings w'here wind effect will 
appear only in deflection errors and can be disre¬ 
garded. However, if this condition cannot be met, 
runs may be made on up and downwind headings, 
and the no-wind MPI computed by using the method 
illastrated in Table 5 of Chapter 5. 


Using a lireliminary sight setting based on experi¬ 
ence or available data, a minimum of three bombs are 
dropped from each of two headings, 180 degrees 
apart. Scoring range errors only, the no-wind MPI 
should be within 50 feet of the point of aim. If this 
is not the case, the .sight may be adjusted; any 
adjustment so made, however, .should be confirmed 
by dropping additional bombs with the new sight 
setting. 

After calibrating by either method, the relation¬ 
ship between the sight setting and the thrust line 
or l)ore sight datum line .should be recorded for 
peilodic checking of the sight alignment. 

Calibration Tests 
for Rocket Tossing 

The same condition of coincidence of sight line 
and flight path is required when tossing rockets as 
in toss bombing. Either of the two methods pre- 


Table 1. Relation between flight path and boresiglit datum line [BSDL] or thrust line for Navy planes. 


Plane 


Weight 

of 

plane 

(Ibl 

(1) 

.\ngle of 

I AS Dive BSDL above 
angle thrust Ime 
(knots) (deg.) (mils) 

(2) 

Flight path 
above B.SDTv 
(theodolite 
tests) 
(mils) 

Flight path 
above 
B.SDL 
(from GIT 
manuals) 
(mils) 

Flight path 
above 
thrust line 
(from wind 
tunnel data) 
(mils) 

Flight path 
above 
thrust line 
[from 

(1) and (2)1 
(mils) 

Referenoe 

No. 

TBM or TBF 

15,000 

300 

30 




30 


126 

TMB-IC 

45473 

14,300 290-300 

18 

0 

29 

28 


29 

132 

TBM-3E 

85862 


315 

30 

0 

35 



35 


F4U, FG, F3A 

12,000 

350 

40 




31 


126 

F4U-1D 

57369 

11,6.50 

340 

35-10 

9 

28 

32 


37 


F4U-1D 

.57181 

12,000 

305 

35 


26 

26 



198(2/21/45) 

F4U-4 

81032 


.320 

30-35 


30 




198(5/8/45) 

F4U-4 

80860 

10,000 

380 

39-43 

28 

35 



63 

94 

F6F 

12,000 

350 

40 




55 


126 

F6F-5 

77555 

10,122 

360 

34-37 

38 

37 

26 


75 

84 

F6F-5 

77555 

10,300 

385 

40-45 

38 

41 

28 


79 

94 

FHF-5 

70179 

12,000 

340 

40 

44 

17 

27 


61 

131 

F6F-5 

72679 

12,400 

320 

30 


27 

23 



198(2/13/45) 

SB2C 

14,000 

320 

40 




9 


126 

SB2C-4 

19717 

13,600 

280 

33-37 

— 23 

32 

27 


9 

165 

SB2C-4 

20354 

12,350 

350 

43-47 

— 23 

45 

43 


22 

78 

SB2C-5 

83135 

'12,100 

315 

32-40 

— 23 

39 

39 


16 

94 



































EXrEKlMENTAL FEI<;HT TEST PROCEDURES 


53 


vioiisly described may he used, although if rockets 
are fired in the determination of a no-wind MPI, a 
sufficient num])er must be used to eliminate the 
effects of ammunition dispersion. 

^ ^ ^ Sight Setting Data 

on \ arioiis Planes Used for Bomb 
and Koeket Tossing 

Sight .setting calibration data for a number of 
Navy airplanes are given in Table 1. It should be 
noted that the longitudinal level line coincides with 
the thrust line in such aircraft as TBM’s, SB2C’s 
and F4U’s, while in the FGF’s, it is along the wing 
chord line which i.s 3 degrees above the thrust line. 

The experimental data ol)tained by diving on the 
theodolite agree fairly well with the theoretical data 
obtained from wind tunnel experiments for the 
TBM’s, F4U-l’s, F()F-5 No. 70179, and the SB2C’s, 
if the expected variation of ±9 mils between planes 
of the same type is considered. The F()F-5 No. 77555 
does not agree with the theoretical value but a 
repetition of theodolite tests checked the exper¬ 
imental figures. 

Better correlation is shown between the theodolite 
sight settings and the sight .settings based on CIT 
angle of attack A alues. The latter were computed 
using equation (82) of Chapter 0, which is based on 
reference 214. Therefore, when no data on individual 
planes are available, a first approximation of the 
correct .sight setting may be obtained from the CIT 
values.*®'^ 


Table 2. Sight settings on P47-D airplanes. 


IMane No. 

Sight setting 
(degrees) 

Plane No. 

Sight setting 
(degree‘s) 

541 

1.3 

360 

2.5 

201 

2.5 

180 

2.5 

281 

2.5 

952 

2.5 

444 

2.0 

295 

2.3 

284 

2.5 

458 

2.5 

141 

2.8 

103 

2.0 

219 

2.8 

334 

2.5 

000 

3.0 

524 

2.5 

485 

2.0 




Table 2 gives sight settings used as a result of 
calibration tests by the bomb dropping method, for 
17 P47-D aircraft in Ninth Air Force in ETO. 
While the majority of settings lie within a fairh' 


narrow range, the extremes agree with a maximum 
anticipated variation of ±1 degree. 

Machine guns arc harmonized at a sight setting 
of 2.0 degree, which is 3 mils above the thrust line. 

Sight .settings 2.0 degrees, or abov'e, indicate a 
nose-up flight attitude, while those below 2.0 de¬ 
grees indicate the plane Hies nose down. 

.\ltimeter Lag Problem 

The use of a pressure altimeter in the bomb director 
creates a problem which can produce errors of 
con.siderable magnitude. The presence of altimeter 
lag causes the bombs to overshoot the target, since 
the range-to-target information set into the com¬ 
puter is longer than the actual range. Solution of 
this problem was not complete at the end of the war. 

One method of mea.suring altimeter lag in a dive 
is to install a flash bulb in the diving plane, connected 
to fire at one of the altimeter contact points (u.sually 
the 4,980-foot point), and then to dive this plane 
past an obseiwation plane flying at constant altitude. 
By observing or photographing the tliving plane 
against the horizon from the observation plane and 
noting where the flash bulb fires with respect to the 
horizon, the altimeter lag at one point in the dive 
can be determined. 

Probably the most accurate anti u.sefid altimeter 
lag experiments were those performed by Tactical 
Test Unit of the Patuxent Naval Air Station under 
BuAer project 3312. The planes being used wei-e 
equipped with Model 0 altimeters which interrupted 
a radio signal at each of the eleven contact points. 
The planes were dived on three photographing 
theodolites on the lange station at Dahlgren, Va. 
The true altitude of the plane at any instant in the 
dive was completed from the theodolite data. By 
.synchronizing the interruption of the plane’s radio 
signal with the theodolite records, the true altitude 
of the plane at each altimeter contact was obtained. 
By comparing the.se data with the altimeter reading 
(corrected for temperature and barometric pressure) 
at each contact point, the altimeter lag in a dive is 
obtained at each contact point. 

Because of the comj^lexity of the.se expei’iments 
and the time required to compute the theodolite 
data, only a limited amount of data was on hand at 
the time NDRC withdrew' from the jjroject. Tests 
on TBM-3E and FfiF-5 planes indicated altimeter 
lags of 3()Q and 300 feet respectively. 















54 


INSTALLATION, OPERATION, ANT) IMAINTENANCE 


It could be expected that if the altimeter las 
should happen to decrease in the ratio of 0/5 be¬ 
tween the first and second altitudes, the true as well 
as the indicated altitudes could be in the correct 
ratio and no error would be introduced in the tossing 
operation. On the other hand, if the lag should in¬ 
crease during the timing run, as it might as the residt 
of an increase in speed and a corresponding change 
in angle of attack, its effect would be exaggerated. 
As an example of what appears to be such an effect, 
it was found that accurate impacts were obtained 
with a particular P-38 when the zero adjustment of 
the altimeter was set off by 1,300 feet, although the 
lag measured for this plane w'as 650 feet. 

Apparently the major cause of these effects lies 
in the aerodynamic conditions at the static orifice. 
Such errors will affect (in dives) not only the bomb 
director equipment but any other device whose 
operation depends on l)arometric altitude or air¬ 
speed. The desirability of a more complete study 
of the phenomenon is obvious. 


4’ OPERATION 

The correct release time for a bomb or torpedo 
tossing attack is a function of the following four 
basic cpiantities: distance from airplane to target, 
velocity of the airplane, angle of dive toward the 
target, and the amount of pull-up acceleration 
(number of g’s). The release time for rocket tossing 
is a function of all the above factors, plus these 
additional ones: propellant temperature prior to 
launching, velocity acquired by the rocket after 
launching, and the length of the launching lanyard 
(for large-caliber rockets). 

By measuring three basic (luantities, the computer 
takes into account the necessary factors to determine 
correctly the release time. These three quantities 
are the time to target (slant range divided by plane 
^Tlocity), measured by the altimeter unit; the dive 
angle, measured by the gyro unit; and the pull-up 
acceleration, measured l)y an accelerometer enclo.sed 
in the computer. 

The trajectory drop of rockets is taken to be a 
linear function of range, i.e., m + nR, times a dive 
angle correction factor. The constant n is determined 
by the type of rocket and the plane velocity, and is 
taken into account by the rocket calibration settings. 
The con.stant m is determined by the setting of the 
temperature-lanyard control. 


^' Optimum Operating Conditions 

The range of flight conditions for which the director 
can be used and the optimum operating conditions 
are given in Table 3 (for rockets). 


Table 3. Operating range for rocket tossing. 



Min. 

Max. 

Optimum 

Dive angle 

15° 

60° 

30° - 45° 

Ma.v. gr’s 

2.5 

6.0 

4 to 6 

.\irspeed 

200 knots 


See below 

Range 



1,500-3,500 yd. 


The rocket calibration adjustment on the computer 
can be set for the most probable speed of attack, 
anti the optimum, of course, will be this speed. In 
the case of rockets at airspeeds below 300 knots, 
the permissible variation from the preset speed is 
about 15 knots. As the airspeed increases, however, 
the adjustment becomes less critical until a variation 
of 30 to 40 knots from a setting of 350-400 knots is 
permissible. 

In tossing bombs there is no manual adjustment 
to compensate in flight for variations in airspeed. 
The maximum usable range is increased greatly, 
however, by the use of higher airspeeds, as shown 
in the table in Chapter 1. The maximum bombing 
range for an airspeed of 400 knots is about 4,500 
yards (at a 40-degree dive angle). The range of 
\'alues of dive angle, pull-up g's and airspeeds as 
shown for rockets will also appl,y for bombs. 

Minimum range for either bombs or rockets is 
determined either by the recovery distance above the 
target, or by the lowest contact on the altimeter. 

4..V2 Adji^istment and Use of the Direetor 

Section 4.3.2 deals w'ith the adjustments which 
must be made, and the procedure followed by the 
pilot in making a successful attack. It covers only 
the operations connected with the director after it is 
installed and tested. Normal procedure for arming 
the plane will be followed in addition to the points 
listed here. 

1 . Adjustment before take off. It will be assumed 
that the plane is armed with both bombs and rockets. 
Each adjustment on the director should then be set 
as shown below. 

Set the altimeter so that it will read zero at the 
altitude of the target. This setting is accomplished 










OPERATION 


55 


by means of the setting knob beside the altimeter 
face. Any method which permits setting to an 
accuracy of about 100 feet is suitable. 

Set the airspeed adjustment on the computer to 
read the speed for which the sight line is parallel 
to the flight line. 

Set the MPI adjustment according to the ballistic 
coefficient of the bombs. Consult Figure 13 in 
Chapter 2 for MPI adjustment for bomb ballistic 
compensation. 

Set the rocket calibration controls on the computer 
according to Table 4, using the speed for which the 
sight line and flight line are parallel. The fine control 
is a vernier on the coarse control, one rotation of the 
fine control (0 to 5) giving the same effect as one 


step, C to D, say, on the coarse control. A clockwise 
rotation of either control shifts the point of impact 
away from the plane. 

Set the temperature and lanyard control to the 
expected temperature of the rocket propellant at 
launching. Table 5 contains the information neces¬ 
sary to do this properly. 

2. Adjustments made during flight. The following 
operations are necessary to prepare the director 
for an attack while the plane is in flight. 

Turn the power switch on at least five minutes, 
before the equipment is to be used, so that the 
tubes w'ill become stabilized. Wlien this sw'itch is off, 
the normal bomb and rocket release circuits are 
o{)erative. 


Table 4. Dial settings for rocket calibration controls.**® 


Plane 

speed 

(knots) 

(TAS) 

3.5-in. AR 

5.0-in. AR 

11.75-in. AR 

5.0-in. HVAR 

2.25-in. AR (Fast) 


Coarse 

Fine 

Coarse 

Fine 

Coarse 

Fine 

Coarse 

Fine 

Coarse 

Fine 

260 

D 

2i 

E 

2 

F 

4 

B 

U 

D 

44 

280 

D 

4 

E 

3f 

F 

4 

B 

34 

E 

14 

300 

E 

1 

F 

t 

F 

4 

C 

f 

E 

34 

320 

E 

2| 

F 

2 

F 

4 

C 

24 

E 

44 

340 

E 

3t 

F 

3i 

F 

4 

C 

4 

F 

14 

360 

E 

5 

F 

4i 

F 

4 

D 

1 

2 

F 

2| 

380 

F 

U 

Cx 

n 

F 

4 

D 

1 1 
i 3 

F 

3| 

400 

F 

2| 

G 

2i 

F 

4 

D 

3 

F 

4f 

420 

F 

3| 

G 

3i 

F 

4 

D 

4 

G 

1 

440 

F 

4! 

G 

44 

F 

4 

D 

5 

G 

24 


Table 5. Settings for temperature and lanyard control.**® 

Propellant 

temperature 

(F) 

Plane* 

velocity 

(knots) 

2.2.5-in. AF (Fast) 

3.5-in. AR 

Dial Settings 
5.0-in. AR 5.0-in, 

, HVAR 

11.75- 
77-in. Lany. 

■in. AR 

36-in. Lany. 


300 

20 

32 

18 

43 

57 

45 

0° 

350 

16 

26 

15 

34 

53 

41 


400 

14 

22 

12 

28 

51 

39 


300 

14 

24 

13 

31 

51 

39 

20° 

350 

11 

19 

10 

24 

49 

37 


400 

9 

16 

9 

20 

47 

35 


300 

9 

16 

8 

20 

46 

34 

40° 

350 

7 

13 

7 

16 

45 

33 


400 

6 

11 

6 

13 

43 

31 


300 

3 

7 

3 

7 

41 

29 

70° 

3.50 

2 

6 

3 

6 

40 

28 


400 

2 

5 

2 

5 

40 

28 


300 

0 

0 

0 

0 

38 

26 

100° 

3.50 

0 

0 

0 

0 

38 

26 


400 

0 

0 

0 

0 

38 

26 


* Use plane velocity nearest the speed at which the flight line and sight line match. 


























56 


l.NS I ALl.A J ION. OPEKATION, AND M AINTENANCE 


If a train of bombs is to be released, adjust the 
stick-length offset so that the first bomb will land 
short of the target by one-half the stick length. 
For single rounds or salvo, this control should be 
set on zero. 

Select bomb or rocket on the transfer switch. If a 
torpedo is to be launched, the transfer switch should 
be set on bomb, and the stick-length offset should be 
turned completely counterclockwise, to the torp 
position. 

The gyro must be uncaged during an attack. If 
there is any doubt as to whether it is erect, it should 
be caged, then uncaged while the plane is in level 
flight. 

3. Sequence of operations during attack. The pilot 
should dive from an altitude which will allow time 
to attain fairly constant speed before the director 
begins to operate. Because of the gyro 60-degree 
bank limitation, the split-*S type of attack may not 
be used. The straight-in approach is not mandatory, 
however, as it is possible to pass the target to one 
side and turn into the attack with a bank of less than 
60 degrees. 

Early ^Vlodel 0 gyros would spill in banks over 
60 degrees. The later Model 1 gyros were modified 
to permit banks up to 85 degrees. This modification 
was also introduced in a number of Model 0 and 
early Model 1 gyros after release to the Service. 

When the point of aim is correct and airspeed has 
stabilized, the pilot should press and hold down the 
bomb release switch and continue the dive toward 
the target with the point of aim steady and the bank 
indicator ball in the center. In a few seconds, the 
pilot’s indicator lamp will light, indicating that the 
pilot should then pull up immediately. The pull-uj) 
should be sudden, and the bank indicator ball should 
be kept in the center until the pilot’s indicator lamp 
goes out. Thereafter the course of the plane is at 
the discretion of the pilot. 

4.3.3 MPI Errors and Remedies 

Use of a director which computes the release time 
reduces to a minimum some of the errors normally 
associated with bombing or forward firing of rockets 
from aircraft, such as incorrect estimation of range, 
dive angle, and airplane speed. However, errors due 
to the following sources are still present. 

1 . Factors other than the director. 

a. Wind or target motion. The pilot must make 
allowance for wind or target motion in the same way 


as for a strafing attack with bullets. The longer 
flight time of bombs and rockets requires a greater 
lead. 

b. Skidding or side slipping. If the pull-up is 
not made in a plane peri)endicidar to the wings, or if 
the airplane skids consistently to one side during the 
approach, a deflection error will result according to 
the amount of side-slip. 

c. Error in sight setting. An error in sight 
.setting will cause the projectile to miss the target 
by the number of mils between the sight line and the 
flight line. 

d. Faulty bomb racks or rocket launchers will 
cause erratic operation Avhich is difficult to trace. 

e. Ammunition dispersion. Errors from this 
source are always present, and account for the larger 
part of the error in rocket firing when this director 
is used. The mean ammunition disjjersion for aircraft 
rockets (Navy) is about 5 mils at opcu-ational plane 
speeds. It decrea.ses with higher airplane .speeds. 

2. Director difficulties and remedies. Some of the 
sources of erratic behavior of the bomb director and 
the suggested remedies are listed below. A compre¬ 
hensive discussion of errors is given in Section 6.4. 

a. d/p/considerably ore?'the target. This may 
be caused by a tumbled or caged gyro, an altimeter 
incorrectly set to read zero at an altitude consider¬ 
ably below that of the target, a sight set incorrectly 
below the flight line, a premature pull-up, or (for 
rockets only) the transfer sicitch .set on bomb. 

b. d/p/con.siderably s/)orf of target. This type 
of inaccuracy may be the result of a tumbled gyro, a 
sight setting above the flight line, an altimeter set at 
zero considerably above the altitude of the target, or 
(for bombs only) the transfer sivitch on rocket. 

c. Errors in deflection may be the residt of a gun- 
sight improperly boresighted in deflection, or an 
improper pull-up. 

d. Small, con.si.stent errors in range MPI (5 to 
10 mils) may be due to a slight error in sight setting 
or to such other cau-ses as variation in rocket launcher 
installations, etc. In bomb tossing they can be 
taken care of by changing the sight setting, or chang¬ 
ing the MPI adjustment, as shown in Figure 3. 
Small range errors in rocket tossing can be corrected 
with the rocket calibration control or with the tempera¬ 
ture and lanyard control. Ten divisions on the latter 
Avill shift the MPI about 10 mils for the slower 
rockets and about 5 mils foi' tlu' 5.0-inch HVAR. 


(^"^SrKiCTETt^^ 






MAIMKNAi\( K 


Clockwise rotation of either of these controls will 
cause the MPI to be longer. The shift in mils 
obtained per 1,000 yards of slant range for a change' 
ot one division on the* fine rocket calibration control 
is given below : 


Coarse setting A It C 1) lO F G 

Mils/1,000 yd 0.4 0.5 0.7 1.0 1.2 1.7 2.0 


d he values are correct for a 35- to 40-degree dive 
angle and 350 knots TAS, and approximatelj’ correct 
for other conditions. 


20 * 



Figure 3. C'alibration curves for MPI dial, bomb 
director Mark 1 Model 1, for various altitudes, dive 
angles, and plane speeds. E.xample: to increase point of 
impact by 4-300 feet at airspeed of 250 knots, dive 
angle of 40 degrees, and pull-up altitude of 6,000 feet, 
read up on chart from 6,000-foot designation to 250- 
knot line for 40-degree dive angle. Read calibration at 
left side of chart, which is 100 feet per scale division. 
Thus -l-300-foot offset requires 4-3 setting of MPI 
control knob. 

Since the effect of the rocket calibration control is 
proportional to range, this control is not ideal in 
compensating for sight errors. Any necessary ad¬ 
justments should be made in the sight setting or, as a 
.second alternative, in the temperature and lanyard 
control. In no case should the rocket calibration 
control be set more than three divisions on the fine 
control from the settings given in Table 4. 


MAINTENANCE 

^ ^ * Field Adjustments 

Maintenance in the field is generally considered 
to be limited to trouble shooting to the extent of 
locating and replacing a faulty component. Beyond 
this, only minor repairs to a faulty component, such 
as replacement of tubes or circuit breakers, or re¬ 
pairs to cables and connectors, should be attempted. 
Major repairs should be undertaken only at proper 
repair depots by competent personnel. 

The following test schedule is recommended for 
use at .squadron levels: 

1. Daily timing of the equipment in the plane bj* 
counting or watching the instrument panel clock. 
This is accomplished in the following manner: 
a. Throw' switch to bomb director position, b. Cage 
gyro. c. Press and hold bomb release button, 
d. Clo.se test sw'itch on pilot’s control box momen¬ 
tarily. Tw'o seconds (or counts) later, close the test 
switch again, at which time the indicator light should 
come on. e. Ten seconds (or counts) later the light 
should go out and the bomb release relay operate, 
f. Release bomb release button and uncage gyro. 

2. Timing of the equipment in the plane using the 
Mark 16 Model 0 test .set after each 25 hours of 
operation. Operation of this equipment is described 
in Section 4.5. 

3. After each 25 hours of operation the gyro 
should be removed from the plane and complete 
instrument shop tests made, including a starting- 
test, erection rates and coasting time tests. At this 
time the resistor strip should be tested for cleanness 
and continuity by using an ohmmeter to measure 
the resistance at all points on the strip. This is done 
by tilting the gyro to cause it to read 60 degrees, 
and with the lever arm in contact with the strip, 
slowly returning the gyro to a level po.sition. Circuit 
continuity should be shown at all positions of the 
arm on the strip. 

4. Trouble shooting. Detailed instructions on 
miscellaneous trouble shooting are given in the 
maintenance manual, reference 232c and in refer¬ 
ence 273. 

Maintenance Experience 

The only available basis for judging the reliability 
of the equipment is the amount of servicing w'hich 
has been required to keep it in operating condition 





















58 


INSTALLATION, OPERATION, AND .MAINTENANCE 


on aircraft. Records of such servicing are available, 
mainly from two sources. (1) Tactical Test Group 
at Naval Air Station, Patuxent, where experimental 
equipment in various stages of development has 
been in use on relatively few planes for seven 
months,and (2) ETO, where 28 sets of 
ecpiipment (of a very early type) were in use under 
field conditions for six months.^®®'^^'* 

It must be considered that all the listed experience 
was gained on either strictly experimental models or 
an interim production type. Obviously, troubles 
are to be expected with such equipment, and since 
corrective measures may be taken as a result of such 
experience it may be assumed that much less diffi¬ 
culty would be encountered with final production 
models. 

1 . The result of six months experience at Naval 
Air Station, Patuxent, is summarized as follows. 

During the period from October 28, 1944, to 
June 1, 1945, no adjustments on computers, such as 
resetting the cathode bias on the release thyratron, 
were found necessary. Definite faults developed in 
only 3 out of 27 computers and onh^ one of these 
was such that it could not readily be repaired. One 
computer had over 100 hours in the air, 4 had over 
60 hours, 10 had over 40 hours, 20 had over 20 hours, 
and 24 had over 10 hours without trouble or ad¬ 
justments. 

No adjustments were made on any altimeters 
during this period. Five out of 26 altimeters were 
removed from planes because of faults. Two altime¬ 
ters had over 100 hours in the air, 10 had over 50 
hours, and 16 had over 25 hours without trouble or 
adjustment. 

No adjustments or repairs were made on g.yros 
during this period. Seven out of 25 gyros were 
removed from planes because of faults (4 mechanical 
faults and 3 electrical). Three gyros had over 
100 hours in the air, 11 over 50 hours, and 19 over 
25 hours without trouble or adjustment. 

2. Following are summaries from reports regarding 
experience in ETO. 

a. About i\Iay 15, 1945, thirteen *P-47 aircraft 
equipped with bomb directors were transferred from 
368th Fighter Group at R-42 Buschwabach, to the 
367th Fighter Group at Y74 near Frankfort. At the 
time of transfer the toss bombing equipment had 
a total flying time of 2,500 hours, ranging from 61 
hours in one aircraft to a maximum of 267 hours 
in another aircraft, as indicated in the accompany¬ 
ing report. 


b. Flying time of bomb director .sets. 


Operational Planes (13) 

Plane 

Installed 

Time (houns) 

D-544 

14 Feb. 

244 


E-458 

2 Mar. 

254 


F-952 

14 Feb. 

241 


H-360 

2 Mar. 

203 


J-040 

14 Feb. 

168 


L-485 

29 Dec. 

267 


L-284 

27 Feb. 

228 


P-589 

29 Dec. 

217 


Q-444 

23 Mar. 

146 


R-103 

30 Mar. 

61 


T-180 

14 Feb. 

197 


U-390 

28 Mar. 

109 


W-007 

23 Mar. 

132 


Planes Lost (6) 

G-258 

25 Feb. 

31 

Crashed 27 March. 

Set total loss. 

J-769 

14 Feb. 

200 * 

Crashed 25 April. 

Set recovered. 

Records 7th. ADG. 

M-734 

29 Dec. 

200 * 

Battle damage. 8 April. 
Records 7th. ADG. 

N-542 

29 Dec. 

53 

Cra.shed 21 March. 

Set ruined. 

T-151 

14 Mar. 

143 

Destroyed in battle, 

24 April. 

Total loss. 

Y-439 

29 Dec. 

50* 

Transferred to U.K. with 
records. 

-584 

29 Dec. 

10 * 

Crashed 3 Feb. Set 
recovered. 




Records at 10th. ADG. 


Total flying time 

3,154 hours. 


* Estimated time as records are not available. 


c. Prior to the transfer indicated in (a) the 
maintenance of the equipment was not excessive^ 
as indicated by the following excerpts from the 
maintenance report of the 396th Squadron of the 
368th Group. 

Twenty-eight sets of Mark 1 Model 0 bomb 
director equipment were originally received for 
installation, of which 20 were installed. Since then, 
3 sets have been lost in crashes, and 2 sets have been 
released for experimental purposes. The sets which 
were installed have been maintained in operational 
status at all times since then. Following is a list of 
all maintenance problems encountered and replace- 















TEST EQUIPMENT 


59 


merits necessary on these sets in approximately 
3 months of use. 

Maintenance required, listed by components, is as 
follows. 

Computer Mark 20 Model 0 
13 A' blocks cleaned 
1 K block wiper loose 

4 voltage regulator tubes replaced 

1 thyratron tube replaced 

2 grid bias adjusted 

1 loose connection inside 

Relay box Mark 11 Model 00 

3 thyratrons replaced 
1 loose wire 

Gxjro Unit Mark 20 Model 0 
12 defective caging handles 

1 defective caging cable 

2 defective caging gears 

5 bad contact on strip 

3 broken wires on strip 

3 pointer arms binding 

4 bad erection rates 
1 out of balance 

1 bearing fell out 
1 defective bearing 

Altimeter Unit Mark 1 Model 0 

6 poor insulation on contact ring 

1 cracked contact ring 

2 poor contacts 

3 stick on contacts 

3 whiskers out of place 
1 adjusting knob binds 

Pilot’s control box 

1 defective DPDT switch 

1 grounded resistor 

Dive angle indicator 

2 burned out 

Signal lights 
2 grounded 

Cables 

5 caused compass deviation 

4 poor insulation at altimeter 

5 wires broken in plugs 

However, when flight operations started again 
at the 367th Group several pilots noticed imme¬ 
diately that their dive angle indicators would not 
function properly. Inspection showed that 9 out of 
the 13 aircraft had gyro trouble, mainly bad rotor 
bearings. 

Of the total of 27 manually caged gyros which 
were brought to the theater, 17 or 18 required 4th 
echelon repairs. 

However, the normal life of the gyro bearings 
should be more than the average 200 hours on these 
planes. Inspection showed that the air filters were 
very dirty. 


3. The most frequent source of trouble was the 
abrasion of the bob-contact and the top segment 
block, which produced an accumulation of metal 
particles sufficient ultimately to short circuit the 
top mica segment. This trouble has been very 
greatly reduced in Model 0 equipments made after 
serial number 266 by using a gold alloy contact in 
place of the phosphor bronze used in the earlier 
computers (see Section 3.5.2). Elimination of 
another source of trouble has been accomplished by 
replacement of hand caging of gyros by an electric 
caging mechanism. 

Trouble from poor altimeter contact ring insula¬ 
tion has been remedied by a redesign of the ring. 

^5 test EQUIPMENT 

‘ Test Unit JVIark 16 Model 0 

The test unit iMark 16 Model 0 was designed to 
incorporate the minimum features necessary for 
field servicing of the bomb director Mark 1 Model 0. 
By using a set of special adapter cables, supplied 
with the unit, tests may be made on the Mark 1 
Model 1 equipment. The principal function of the 
unit is to put an accurately timed pulse into the 
computer and measure the resulting output time. 
For this purpose an a-c operated electric timer, 
Type SI, of the Standard Electric Time Co., 
Springfield, Mass., was modified to close one pair of 
contacts each second. This may be used to introduce 
timing pulses exactly one second apart. A second 
pair of contacts is used to flash a neon lamp each 
time the first pair is closed. 

The schematic arrangement of the timer is shown 
in Figure 4. If switch *82 is held down for one flash, 
up for the next, and down for a third, a 2-second 
signal will be introduced. 

The timer actuated by the J or signal light circuit, 
measures the time from second altimeter contact to 
release. 

The timer operates on 110 volts alternating 
current at a nominal 60 cycles. Since time ratios are 
the only precise requirements, exact frequency con¬ 
trol is not essential. The unit may be operated either 
directly from alternating current, or by 24 to 30 
volts direct current, by use of a vibrator-transformer 
combination. 

In addition to operating the computer, as dis¬ 
cussed above, the test unit has a voltmeter for 







GO 


INSTALLATION, OPERATION, AND MAINTENANCE 



Figure 4. 


Schematic circuit diagram of field test unit Mark 16 Model 0. 















































































































































































































































TEST EQUIPMENT 


(31 


checking the supply voltage, and a bridge for adjust¬ 
ing the gyro end resistor. 

Detailed operating instructions for the equipment 
were supplied with it.®" 

" ' Test Unit Mark 17 Model 0 

This test unit, Mark 17 Model 0 (TS-362/ASG-10), 
is considerably more elaborate than the test unit 
Mark 16. It incorporates the timing system similar 
to that of the Mark 16 but the a-c timer power is 
deriv’ed solely from a d-c operated vibrator inverter. 
Weighing approximately forty pounds, it is more a 
complete bench tester rather than a portable set 
to be used in aircraft.-®- It incorporates the follow¬ 
ing features. 

1. A timer which may introduce an accurately 
timed input and measure the output time. 


2. Pilot control box with MPI settings of 0 and —5, 
and a stick offset of 10. A double-throw switch may 
throw'' in either the internal “pilot control box” or an 
externally connected one. 

3. A set of lights to indicate continuity of the 
eage-uncage circuits, the solenoid circuit, a terminal 
to check resistance of the gyro end resistor, and a 
switch to open the pointer circuit so that the 0.33- 
megohm resistor in the computer may be checked 
for continuity. 

4. Signal light. 

5. Bomb release indicator light. 

6. A switch to enable an adjustment to be made 
of the grid bias of the output thyratron. 

7. A simple megohm meter with a range of 2 to 
1,000 megohms. 

8. A thyratron tester which can measure grid 
current and firing bias. 




Chapter 5 

EVALUATION OF THE TOSS TECHNIQUE 


5 » TOSS BOMBING FIELD TESTS'^ 

S ECTION 5.1 SUMMARIZES all significant flight tests 
on production equipment, Mark 1 Model 0 
and jMark 1 Model 1, together with tests on some 
special applications. The major portion of the 
testing program was carried out at the Naval Air 
Station, Patuxent River, Maryland, by Navy 
personnel, with technical assistance from Division 4, 
NDRC. About 5,000 bombs were dropped at this 
station between October, 1944, and August, 1945. 
During the same period, tests were conducted at the 
Antisubmarine Development Detachment, Naval 
Air Station, Quonset, Rhode Island; but the smaller 
number of planes used, and the generally unfavor¬ 
able weather conditions prevalent at that station, 
resulted in a smaller amount of data. A limited 
amount of flight testing was also done at other naval 
stations and army fields. 

In this summary, tests are arbitrarily classified 
into the following groups: (I) Tactical evaluation 
tests, (2) equipment evaluation tests, (3) special tests. 

s.i.i Tactical Evaluation Tests 

A measure of the effectiveness of the Mark 1 
Bomb Director is given by the results of pilots’ 
evaluation tests-^^^‘‘® carried out at the Naval Air 
Station, Patuxent River, during the period October 
1944 to August 1945. The object of the test was to 
obtain the highest percentage of target hits at the 
particular slant ranges and dive angles designated 
for each group of flights, the values of which' fell 
within the tactical limitations of both plane and 
equipment. In all cases, correction for wind error 
was introduced by the pilot by aiming off the target, 
using the sight mil rings as reference. The amount 
of aim offset for the first bomb of a flight was calcu¬ 
lated by the pilot, using the wind correction charts 
and local aerological data. The location of the bomb 
impact determined any correction necessary in the 
aiming allowance for the re.st of the bombs. Usually 

^Sections 5.1 and 5.2 were written by Emma U. Rotor of 
the Ordnance Development Division, National Bureau of 
Standards. 


five or six bombs were dropped on each flight. The 
bombing rums were made upwind, downwind, or 
crosswind to facilitate wind correction. In general, 
the bombing approach was made in a slight turn up 
to the pushover point in order to keep the target in 
sight. When the proper position tvas attained, the 
nose w'as swung over the target and a straight push¬ 
over entry made into the dive. Pushover was usually 
started at an altitude about 5,000 feet above the 
pull-up altitude in order to reach the desired speed. 

Test features are summarized in Table 1. Previous 
to the pilots’ evaluation tests, all planes underwent 
sight calibration flights (see Section 4.2.1). Two 
tai-gets were used: (1) Polnt-No-Point target — a 
platform 30 feet square in shallow w'ater with pile 
markers giving reference points at 50, 100, 200, and 
300 feet radius from the center in four directions 
90 degrees apart; (2) Sharp’s Island target — a 
platform 10 feet square in shallow w'ater with pile 
markers giving a circular reference 15 feet in radius 
from the center, plus pile markers giving reference 
points at 50, 100, 200, and 300 feet radius from the 
center in four directions 90 degrees apart, plus 
additional pile markers at 100-foot intervals on the 
north leg of the target extending to a distance of 
1,000 feet from the center. Impact data were based 
on either visual or photographic observations. In 
the first case, recorded data were obtained inde¬ 
pendently by both pilot and observer; in the second 
case, a photo-observation plane accompanied the 
test plane and photographed each impact. The 
accuracy of measurements in the latter case was 
about plus or minus 5 feet. A comparison of the 
values obtained from photographic assessment and 
from \dsual observation of the same impacts showed 
no large discrepancies, the difference rarely exceed¬ 
ing 25 feet and averaging about 15 feet. Dive angles 
between altitude points were read by the observer 
from the gyro. When this was impossible because 
of the location of the gyro, dive angles were read 
by the pilot or an observer from a dive angle repeater 
instrument especially installed for the purpose. In 
the first case, measurements wmre accurate to about 
plus or minus 3 degrees; in the second case, the accu¬ 
racy w'as slightly less. Indicated airspeeds w^ere 
read by the pilot from his instrument panel in the 


62 



Fable 1. Pilots’ evaluation tests. 


63 


TOSS BOMBING FIELD TESTS 


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6-1 


EVALUATION OF THE TOSS TECHNIQUE 


early part of his pull-up and were accurate to about 
plus or minus 10 knots. The maximum acceleration 
reached during pull-up was read by the pilot from 
the plane accelerometer and was accurate to about 
plus or minus 0.2^. The lowest altitude reached in 
pull-up was read by the pilot or observer and was 
accurate to about plus or minus 200 feet. 

Test results are illustrated in Figure 4 of Chapter 1, 
wherein are shown impact points of 747 bombs 
<lropped from medium slant ranges, and in Figure 1, 


FEET 
100 — 


0 — 


100 — 


200 — 


O o 


o 
o o 


o o 



— 100 


-0 


— 100 


100 


I 

100 


— 200 
FEET 


RADIAL ERRORS 
(FEET) 





Figure 2. Distribution of impact errors in feet of 747 
bombs tossed at slant ranges of 5,400 to 9,300 feet. (See 
Figure 4 of Chapter 1 for impact pattern.) 



FEET 


Figure 1. Impact pattern of 133 bombs dropped in 
pilots’ evaluation tests at Naval Air Station, Patuxent 
River, Maryland, using short slant ranges of 5,400 to 
9,300 feet. (See Figure 4 of Chapter 1 for impact pat¬ 
tern at longer ranges.) 

which gives the impact points of 133 bombs dropped 
from short slant ranges. A number of bombs were 
not scored for such reasons as defective bomb racks, 
defective bombs, caged gyro, spilled gyro, defective 
gunsight, poor visibility, slant ranges, and plane 
speeds being outside the limitations of the ecpiipment. 

Further analysis of the data is given in tabulated 
form in Table 2 and graphically in Figures 2 and 3. 
Bombs which hit the center 30-foot square platform 
of Point-No-Point target were given a radial error of 
11 feet, a 7.8-foot range error and a 7.8-foot deflec¬ 
tion error, since in the case of a hit the actual distance 


RADIAL ERRORS 
(MILS) 





-i30*/. 


- 20 % 


10% 


0 % 


- 20 % 


10 % 


0 % 


- 20 % 


- 10 % 


0 % 


Figure 3. Distribution of impact errors in mils (same 
bombs as in Figure 2.) 



































































































TOSS BOMBING FIELD TESTS 


05 


from the center of the target could not be deter¬ 
mined. Mil errors were calculated on a plane at the 
target perpendicular to the line of sight by the fol¬ 
lowing formulas: 

Range mil error = 

Ground error in feet X Sine of d ive angle X 1000 
Slant range at second altitude 

Deflection mil error = .Ground error in feet X 1000 . 

Slant range at second altitude 

(Radial mil error)^ = 

(Range mil error)- -f (Deflection mil error)-. 


of the SB2C-4 and F4U-1D ]Dlanes, provide some 
means of comparing the relative accuracy of dive 
boml)ing with that of the toss bombing technique 
under approximately the same conditions of re- 
lease.-^“'-^®'‘ Project PTR-1204, NAS Patuxent, con¬ 
sisted of dive bombing tests at an average release 
altitude of 2,000 feet at steep dive angles. taking 
the results of the pilots’ evaluation tests at a second 
or pull-up altitude of 2,000 feet, comparison as shown 
in Table 3 is possible. It should be noted, howevei’. 


Table 2. Results of pilots’ evaluation tests. 


Total number of bombs: 747 


(a) At medium slant ranges 


Slant range: 5,400-9,300 ft 


Average 

error 

Median (absolute) erroi 


ft 

mils 

ft 

mils 

Radial 

118 

13.5 

100 11.5 

Range 

79 

7.2 

61 5.8 

Deflection 

70 

9.8 

52 7.8 


Results according to direction of plane 

approach 




Crosswind Downwind 

Cl)wind 

.\vg. radial error (mils) 

14.2 

12.7 

13.4 

.\vg. range error (mils) 

7.0 

6.7 

7.3 

.\vg. deflection error (mils) 

10.5 

9.1 

9.9 

Number of bombs 


289 

291 

1.59 


Total number of bombs: 133 


(b) At short slant ranges 


Slant range: 3.500-4,000 ft 


Average error 

Median (abs 

olute) error 


ft 

mils 

ft 

mils 

Radial 

53 

10.6 

50 

7.6 

Range 

37 

5.3 

18 

2.6 

Deflection 

28 

7.5 

S 

2.1 


(c) Kesulis (a) and (b) according to slant range 


Slant range at 
second altitude 

Number of bombs 

Average radial ( 
ft mils 

7,100-9,300 ft 

375 

134 

13.3 

5,400-7,000 ft 

372 

101 

13.7 

3,500-4,000 ft 

133 

53 

10.6 


Comparison of Toss Bombing with Standard Dive 
Bombing. The data furnished by the pilots’ evalua¬ 
tion tests at low altitudes when used in conjunction 
with the results of Project PTR-1204, a test to 
determine the comparative dive bombing accuracy 


that the dive angles in toss bombing were between 
30 and 45 degrees, whereas those in dive bombing 
were much steeper, so that although altitudes 
involved are comparable, the slant ranges for toss 
bombing were considerably longer. 




























m 


EVALUATION OF THE TOSS TECHNIQUE 


Low Ceiling The SB2C-3, SB2C-4 and 

F4U-1D planes used in the pilots’ evaluation tests 
made special flights to determine the minimum 
veiling conditions under which the toss bombing 
maneuver could be successfully made without 

Table 3. Comparison of toss bombing with ordinary 
dive bombing. 

Total average radial error in dive bombing for 4 pilots, 
average release altitude 2,000 ft (270 bombs) 83 ft 

Total average radial error in toss bombing for 3 pilots, 

second altitude 2,000 ft (133 bombs) 53 ft 

Improvement in bombing efficiency = (83)*/(53)2 = 2.5 times* 
Bombs required for given effect using toss bombing = 40% 
of those needed using conventional dive bombing. 


sacrificing accuracy. Results showed that low ceiling 
attacks could be accurately made in both types of 
planes from a starting altitude of 3,000 feet in level 
flight at high entry speed (200 or more knots) 
with recovery from the dive above 800 feet. A dive 
angle of 25 to 30 degrees with a speed of 280 knots 
could be attained if the 1,660/1,390 feet altitude 
contacts were used. 

Evaluation Tests in Army Aircraft, Eglin Field, 
Florida.-=^ During the period January 24 to May 12, 


fighter-type aircraft for release altitudes of 4,000 feet 
and above, and to determine what improvement, 
if any, the l)omb director gave over standard dive 
bombing at the same altitudes of release. The boml) 
director was found unsuitable in P-38J aircraft 
because the pitot static installation resulted in 
excessive altimeter lag — more than 600 feet. Toss 
bombing with the P-5 ID aircraft was successful but 
tests were discontinued because the Model 0 equip¬ 
ment, installed between the engine and fire wall, was 
l)eing subjected to high ambient temperatures. 
(The dimensions of the Model 1 equipment permit 
a more suitable location.) Most of the tests were 
therefore made in a P-47D aircraft. 

Six pilots, three experienced in dive bombing and 
three inexperienced, participated in the tests. Three 
release altitudes were used — 4,000, 6,000, and 
8,000 feet, approximately—corresponding to second- 
altitude contacts at 4,980, 7,160, and 8,600 feet, 
respectively. Average dive angle was about 40 de¬ 
grees; indicated airspeed, 400 to 440 mph. Each 
pilot made two releases from a P-38 plane using 
conventional dive bombing and two releases from a 
P-47 plane equipped with the bomb director. Differ¬ 
ent headings were used for each of the two runs in a 
flight. No pilot made more than one flight in the 


Table 4. Results of comparison test — Eglin Field, Florida. 



4,000 ft 

6,000 

ft 

8,000 

ft 


P-38 

P-47 

P-38 

P-47 

P-38 

P-47 


No comput¬ 

Bomb 

No comput¬ 

Bomb 

No comput¬ 

Bomb 

Release altitude 

ing sight 

director 

ing sight 

director 

ing sight 

director 

Number of releases 

106 

129 

65 

75 

52 

85 

Average range error 

346 ft 

211 ft 

414 ft 

301 ft 

497 ft 

464 ft 

Average deflection error 

167 ft 

178 ft 

274 ft 

238 ft 

292 ft 

283 ft 

Average circular error 

416 ft 

306 ft 

542 ft 

433 ft 

632 ft 

591 ft 

Circular probable error 

382 ft 

302 ft 

500 ft 

409 ft 

589 ft 

510 ft 

Range MPI 

-t- 143 ft 

- 28 ft 

4- 55 ft 

- 62 ft 

- 116 ft 

- 182 ft 

Deflection AIPI 

- 12 ft 

+ 5 ft 

- 60 ft 

-33 ft 

- 46 ft 

- 130 ft 

Percentage of hits (100-ft radius) 

9.4 

14.0 

1.9 

4.0 

1.9 

4.7 

The equipment in the P-47 plane 

was a Mark 1 

Model 0 bomb director. Bombs used were 

M38A2, 100-lb practice bombs. 

Dive angles and indicated air speeds increased from 37 degrees, 
at 8,000-ft release altitude. 

400 mph at 4,000-ft release altitude to 42 degrees. 

440 mph 


1945, the Mark 1 Model 0 bomb director was tested same plane on the same morning or afternoon, 
in P-47D, P-38J and P-51D aircraft at Eglin Field, Missions were repeated daily until a representative 
Florida. The tests were conducted to determine the sample at the three altitudes was obtained, 
accuracy and practicability of the bomb director in The results of the tests are summarized in Table 4. 















TOSS BOMBING FIELD TESTS 


67 


On the basis of the circular probable error [CPE], the 
bomb director was found to be more accurate by 
20.9, 18.2, and 13.4 per cent at 4,000, 6,000, and 
8,000 feet release altitude, respectively. The average 
dive angles used ranged from 37 degrees at 4,000 feet 
to 42 degrees at 8,000 feet. These are based on 


on the whole, the bomb director scores of the inex¬ 
perienced pilots were 29 per cent poorer than those 
of the experienced pilots. The scores obtained at 
Eglin Field are definitely less favoi-able than those 
obtained in pilots’ evaluation tests at Patuxent 
Naval Air Station; however, they are not surpri.'^ing 


+ 300 


+ 200 



Figure 4. Plot of all (39) bombs identified in combat toss bombing missions with P-47 aircraft, 368th Fighter Group, 
Nineteenth Tactical Air Command, Ninth Air Force. Average conditions at release: altitude 3,000 feet, dive angle 40 
degrees, speed 350 to 400 mph, and range 4,700 feet. The 50 per cent circle was 200 feet for all bombs, including 10 gross 
errors not shown. (Diagram reproduced from ORS report, reference 269.) 


pilots’ estimates minus 5 degrees, the approximate 
amount of pilot e.stimate error. These give second- 
altitude slant ranges of 8,300 feet at the low altitude 
and 13,000 feet at the high altitude. The use of dive 
angles shallower than those required for accurate 
operation of the bomb director at high altitudes 
caused many bombs to fall short by large amounts. 
This was especial!}' true of the inexperienced pilots; 


in view of the particular test conditions used. 

While it is true that a strict tactical evaluation 
of the bomb director should give the results of flights 
under comlmt conditions, an analysis of flights con¬ 
ducted at testing stations can give a measure of the 
expected performance of the equipment in Service 
use. The jiilots’ evaluation te.sts at Patuxent may 
be said to represent the expected results under 












68 


EVALLIA I ION OF THE TOSS TECHNIQUE 


optimum conditions — the same pilot and plane 
make five or six successive runs on the target and 
thus can benefit from the information given by 
the first bomb impacts as regards the amount of 


of the group.'’ Therefore, it is not unreasonable to 
expect that in Service use, the performance of the 
bomb director would be somewhere between those 
indicated by the results of the Patuxent and Eglin 


4-300' 


+ 200 



Figure 5. Plot of all (25) bombs scored, after discarding); releases in which bombs hung up, or where pilot aimed at wrong 
target, etc. The 50 per cent circle was 145 feet. (See Figure 4 for average conditions at release and for plot of all iden¬ 
tified bombs.) 


aim offset needed to compensate for wind. On the 
other hand, the tests conducted at Eglin Field might 
be said to represent the opposite set of conditions. 
Here, the pilot makes only two successive runs, with 
different headings, so that he has to base his aim 
offset estimates purely on whatever aerological data 
are available. The toss bombing te'chnique is de¬ 
signed for use in squadron attack and the location 
of the bomb dropped by the leader would give the 
required wind compensation information to the rest 


Field tests. The results of limited operational use do 
lie between these extremes, as shown in the next 
paragraph. 

^ In the course of the Eglin Field ev'aluation project, two- 
plane team tos.s bombing wa.s given a limited test. The 
first pilot aimed on the target, the second observed the 
impact and made his corrected run on the same heading. 
Eighteen pairs of bombs dropped from 4.000 feet release 
altitude by four different teams gave an average circular error 
of 281 feet for the second bomb as compared to 493 feet 
for the uncorrected bomb. 




















TOSS BOMBING FIELD TESTS 


69 


Operational Evaluatioii hij Ninth Air Force. Thir¬ 
teen operational missions using Model 0 bomb tossing 
equipment were carried out during the last half of 
March 1945. These were conducted over Germany 
by the 3()8th Fighter Group of the Nineteenth 
Tactical Air Command of the Ninth Air Force. 
Evaluation of the missions was made by the Opera¬ 
tional Research Section of the Ninth Air Force.^®* 
Photographic coverage was made on all missions 
but only four of these were assessable. From four 
to twelve P-47 aircraft carrying two bombs apiece 
participated in each mission. 

The impact distributions of the four assessable 
missions are plotted in Figure 4, which shows a CPE 
about the target of 200 feet (Figure 4 does not show 
10 gross errors). It was established that in a few 
cases, the bombs hung up momentarily in the racks 
or the pilots had aimed at the wrong target. If these 
rounds are discarded, the impact pattern shown in 
Figure 5 is obtained. Here the CPE is 145 feet. 
Figures 4 and 5 are from the ORS report-®® referred 
to above. 

The general conclusion of this report was that 
further data were needed to establish the possible 
advantage ratio of the bomb tossing equipment in 
combat. However, it was estimated that with the 
]\Iodel 0 ecpiipment, the accuracy would not exceed 
that shown in Figures 4 and 5. The reference report 
noted that the reaction of the aircraft pilots to the 
equipment was very favorable. Their noncjuantita- 
tive evaluation was that the accuracy of fighter- 
bomber operations would be appreciably improved 
with the tossing equipment. 


satisfactory in all cases where the point of impact was 
within the area which conditions of the particular 
test indicated as proper. This does not mean that all 
satisfactory impacts fell within any fixed distance 
from the target. In cases wdiere bombs w^ere dropped 
in tests involving upwind and downwind runs, with 
no adjustments made in the equipment or gunsight 
to bring the impact point nearer the target, the 
bombs should fall in approximately the same place 
regardless of the heading, provided the instrument 
settings are constant and no sudden variation in wind 
conditions occurs. Such impacts are considered 
satisfactory, although with respect to the target or 
point of aim, they may be a considerable plus or 
minus distance away. Figure 6 is an illustration of 
impacts of this type. In general, unsatisfactory drops 
are easily classified, normally deviating from the 
common impact area by a considerable amount. 
In most cases, they miss the common impact area 
by several hundred feet. 


340° 


AVERAGE WIND 
/20MPH FROM 360* 


200 ' 




100 ' 


POINT OF AIM 


100 ' 200 ' 



I 


100 ' 

200 ' 

300' 


® Equipment Evaluation Tests 


160 * 


Overall Operation of the Mark 1 
Bomb Director 

A measure of the reliability of the Mark 1 bomb 
director is afforded by studying the results of all 
recorded flights made wdth this equipment at the 
Naval Air Station, Patuxent River. ®«.«.®®.“.®®.®®.^®.®®. 
®®.®^ Since these flights were made under all condi¬ 
tions, varying according to the tj^pe of test being 
conducted, results of the group as a wRole cannot be 
analyzed from the standpoint of location of no-wind 
MPI, magnitude of radial error, dispersion, or other 
similar means of scoring. 

The operation of the equipment w'as considered 


Figure 6. Results of typical test flight to check no-wind 
MPI. Shown are bomb impacts of two flights made in 
quick succession. Slant range at second altitude was 
approximately 6,000 feet. Each flight consisted of 5 
runs, runs being made with alternate plane headmgs 
180 degrees apart. Small arrows indicate plane heading 
used for each run. (For methods of computing no-w4nd 
MPI, .see Table 5.) 

The method of calculating the no-wind mean point 
of impact [MPI] is demonstrated in Table 5, using 
the data from Figure G. 

Since the object of this survey is the appraisal of 
the functioning of the Mark 1 bomb director, obvi¬ 
ously impacts w'hich are unsatisfactory due to some 
factor outside the equipment were not scored. Some 





70 


EVALUATION OF THE TOSS TECHNIQUE 


of these factors are rack lag, frozen bombs, pilot 
error, and adverse weather conditions, such as clouds 
hiding the target during the bombing run. In many 
of the tests, especially during the early part of the 


This was done since it is often true that malfunction¬ 
ing which occurs in flights is not readily duplicated 
in laboratory tests and thus its cause can be more 
readily diagnosed through flight tests. This lowers a 


Table 5. Methods of computing no-wind MPI. 


Plane 

heading 

Range 

error 

Deflection 

error 

No-wind range 
impacts (computed) 

Alternative method of 
computing no-wund MPI 

160“ 

+ 200 

150R \ 

- 18 ft 


340“ 

- 235 

65L/ 



160“ 

-f 285 

140R 1 


Average impact 

340“ 

- 325 

105L: 

- 35 ft 

point for runs 

160“ 

-f 225 

115R j 


at 340“ heading — 215 ft 

340“ 

- 160 

115L 1 

+ 8 ft 

Average impact 

160“ 

-1- 175 

125R J 


point for runs 





at 160“ heading + 235 ft 

340“ 

- 140 

llOLl 



160“ 

+ 260 

135R ^ 

+ 62 ft 


160“ 

+ 265 

125R J 

— 




No-wind MPI 

+ 8 ft 

No-wind MPI + 10 ft 


Table 6 

Date of tests: November 7, 1944, to .July 31, 1945. 

Planes: 15, as follows: two SB2C-3’s, four SB2C-4’s, one 
SB2C-5, one F4U-1D, one F4U-4, two P-47’s, two F6F-5’s, 
one TBM-lC, and one TBM-3E. 


Total number of bombs to.ssed.4,226 

Total number of bombs scored.3,998 

Total number of satisfactory impacts.3,883 or 

97.1%. 


Total number of unsatisfactory drops, 115 or 2.9%, as 
follows: 

89, or 2.2%, premature releases 
8, or 0.2%, late releases 
12, or 0.3%, defective gyro oi)eration 
6, or 0.2%, defective altimeter operation. 

Most of these unsatisfactory operations occurred during 
the early part of the developmental i)rogram. Their causes, 
being mainly small defects in design and workmanship, were 
localized and eliminated. 


Total number of bombs not scored, 228, as follows: 

35% Unobserved impact point. 

24% Wrong technique, e.g., premature pull-up, chang¬ 
ing dive angle during aiming run, leaving gyro 
caged,low speed. 

18% Defects outside of toss bombing ecjuipment, e.g., 
rack lag, frozen bombs, bomb bay doors closed. 

15% Adverse weather conditions — poor visibility. 

6% Bombs dropped in salvo of two or more, only one 
of which was scored. 

2% Bomb director switch in off position. 


production program, it was found desirable to con¬ 
tinue, for a limited time at least, the use of equipment 
which occasionally or even frequently malfunctioned. 


“score” but is justified from a developmental 
standpoint. 

Table 6 summarizes the results of tests with the 
Mark I bomb director at NAS, Patu.xent, from the 
point of \dew of satisfactory operation of the equip¬ 
ment. 

Constancy of No-Wind MPI 

Mark 1 Model 0 Equipment. Tests were carried 
out at NAS, Patuxent, during November and 
December 1944 to determine the effect of changing 
slant range and dive angle on the no-wind AIPI.^^.®- 
Prior to the tests proper, each plane made calibration 
flights at 3,450 feet second altitude and 40 degrees 
dive angle. The sight and MPI adjustment settings 
which placed the no-w'ind MPI reasonably near the 
target under these conditions w'ere adopted for the 
whole test. In no ca.se was any correction for wind 
introduced by the pilot. The plane approached the 
target alternately from two opposite directions. A 
no-w'ind impact w'as calculated for each pair of drops 
at alternate headings, using the method illustrated in 
Table 5. The no-wind MPI was computed for each 
combination of dive angle and .second altitude by 
taking the algeliraic average of all no-wind impacts 
at this dive angle and altitude. The mean absolute 
error about the no-wdnd MPI was computed by 
using standard equations based on normal distribu¬ 
tion laws, and was taken as 0.8 of the standard error. 

















TOSS BOMBING FIELD TESTS 


71 


The corresponding mil value for each impact, pro¬ 
jected on a. plane perpendicidar to the line of sight, 
was computed, and similar calculations made. 

Test results are summarized in Table 7. It is 
noted that with the variations of dive angle and 
slant range defined by the test, the shift of no-wind 
MPI was insignificant in magnitude and smaller 
than variations introduced by, say, air l)umps. It is 


noted, however, that (1) the MPI tends to shift in a 
minus direction as the altitude increased, the dive 
angle remaining constant, and (2) the MPI tends to 
shift in a minus direction as the dive angle is 
decreased from 40 to 20 degrees, the slant range re¬ 
maining approximately the same. 

Mark 1 Model 1 Equipment. The same test was 
carried out on a set of Mark 1 Model 1 equipment in 


Table 7. No-wind MPI tests with Mark 1 Model 0 bomb director. 


Plane 

Settings 

2nd 

Avg. 

dive 

angle 

.4vg. slant 
range at 
2nd alt. 

Avg. 
IAS at 
pull-out 
(knots) 

No. 

of 

bombs 

No. of 
no-wind 
impacts 

No-wind 

.MPI 

(ft) 

Mean abs. 
dispersion 

(ft) 

No-wind 

MPI 

Mean abs. 
dispersion 
(mils) 

Sight 

MPI 

alt. 

(mils) 

SB2C-4 

19.5° 

0 

4,150 

38° 

6,700 

320 

19 

9 

+ 1 

62 

+ 2.6 

4.7 

#20381 



2,880 

37° 

4,800 

320 

19 

7 

-f 98 

40 

+ 17.1 

3.8 




2,000 

23° 

5,100 

310 

18 

8 

- 11 

44 

+ 0.9 

4.7 




1,390 

22° 

3,700 

310 

16 

7 

-f 88 

39 

-f 9.9 

4.7 

SB2C-4 

19.5° 

-b 5 

4,150 

38° 

6,700 

315 

15 

6 

- 53 

46 

- 0.2 

6.9 

#20354 



2,880 

35° 

5,000 

325 

15 

7 

- 35 

46 

-f- 3.4 

5.3 




2,000 

23° 

5,100 

315 

15 

7 

- 58 

53 

- 4.8 

3.2 




1,390 

21° 

3,900 

315 

13 

4 

- 23 

71 

- 1.2 

6.6 

SB2C-3 

19.5° 

0 

4,150 

39° 

6,600 

315 

14 

6 

- 45 

38 

- 0.3 

5.7 

#18604 



2,880 

38° 

4,700 

320 

18 

7 

+ 32 

45 

+ 7.4 

7.0 




2,000 

23° 

5,100 

310 

16 

7 

— 102 

80 

- 6.8 

6.9 




1,390 

24° 

3,400 

310 

16 

7 

- 49 

70 

- 3.4 

5.2 

F6F-5 

47.5° 

- 5 

4,150 

42° 

6,200 

365 

16 

8 

-f- 25 

26 

+ 3.7 

2.8 

#70179 



2,880 

40° 

4,500 

360 

8 

4 

- 9 

10 

- 0.6 

1.6 




2,000 

21° 

5,600 

340 

10 

5 

- 63 

60 

- 3.7 

3.5 




1,390 

21° 

3,900 

340 

10 

4 

-f- 48 

8 

-f 5.6 

3.0 

SB2C-4 

19° 

0 

7,160 

43° 

10, .500 

320 

15 

6 

- 44 

104 

+ 0.1 

6.6 

#20381 



5,970 

41° 

9,100 

315 

20 

7 

- 25 

73 

- 1.1 

5.0 




4,980 

38° 

8,100 

325 

13 

5 

- 23 

67 

- 0.2 

6.5 




2,880 

37° 

4,800 

300 

10 

4 

+ 14 

14 

+ 1.9 

1.6 

SB2C-4 

19° 

0 

5,970 

44° 

8,600 

340 

16 

8 

- 31 

75 

+ 0.4 

6.4 

#20354 



4,980 

44° 

7,200 

340 

17 

7 

+ 25 

35 

+ 6.1 

2.5 




2,880 

38° 

4,700 

310 

12 

5 

-f 94 

18 

+ 12.3 

1.1 


Table 8. Range no-wind MPI tests with Mark 1 Model 1 bomb director. 


Plane: SB2C-4 #20381 MPI setting: 0 Sight setting: 17.5° 




.\vg. slant 

Avg. 







2nd 

Avg. 

range at 

IAS at 

No. 

No. of 

No-wind 

Mean abs. 

No-wind 

Mean abs. 

alt. 

dive 

2nd alt. 

pull-out 

of 

no-wind 

MIT 

dispersion 

MPI 

dispersion 

(ft) 

angle 

(ft) 

(knots) 

bombs 

impacts 

(ft) 

(ft) 

(mils) 

(mils) 

2,000 

22° 

5,300 

300 

42 

20 

- 16 

35 

- 0.3 

2.5 

2,400 

22° 

6,400 

300 

30 

14 

- 173* 

51 

- 9.3 

4.5 

3,450 

43° 

5,000 

325 

10 

5 

+ 7 

37 

-f 1.5 

4.3 

4,150 

41° 

6,300 

335 

10 

5 

-f 24 

35 

-b 2.9 

3.5 

4,980 

41° 

7,600 

320 

12 

5 

+ 1 

31 

+ 1.4 

4.3 

5’970 

36° 

10,100 

330 

10 

5 

+ 37 

58 

-b 2.0 

2.8 

7,160 

40° 

11,100 

325 

10 

5 

-t- 83 

34 

-b 5.0 

1.5 


♦Short MPI explained by combined effects of change in angle of attack (sight was calibrated at 40“) air resistance, relatively low speed at 
slant range involved, limitations of function. Subsequent flights with the MPI dial setting moved to -|-2 gave a range no-wind, .MPI of -11 feet 
(-0.3 mil) for 34 bombs. Mean absolute dispersion was 49 feet (3.4 mils). 











































72 


EVALUATION OF THE TOSS TECHNIQUE 


an SB2C-4 airplane during June and July 1945."® 
The test procedure was the same as outlined above, 
with improvements in some test features. For 
example, bombs with better ballistic coefficient 
were used, ten bombs were dropped on each flight, 
and the bomb racks had been especially wired so 
that it was possible to measure the time lag between 
the reception of the release pulse and the actual time 
of release of the bomb.'°® It was thus possible to 
discard several abnormal impacts which were due to 
excessive rack lag. 

The test results are given in Table 8. The no-wind 
MPI remained fairly constant, except for the group 
of bombs dropped at 2,400 feet second altitude, 
20 degrees dive angle. The short MPI under these 
conditions may be explained by the combined effect 
of several factors (see Table 8). There was no tend¬ 
ency for the no-wind MPI to shift in a minus 
direction as the altitude was increased, dive angle 
remaining constant; on the contrary, there seemed to 
be an unexplained positive shift at the higher 
altitudes. 

Special Tests 

Tests at NAS, Quonset, Rhode Island 

In this heading are placed the tests carried out at 
the Antisubmarine Development Detachment, Naval 
Air Station, Quonset, Rhode Island, for the purpose 
of determining the value of the Mark 1 bomb director 
in relation to other forms of bombing attack on 
submarines ^md comparable targets. The low- 
altitude tests are divided into two groups, the first 
com])rising flights in which bombs alone were tossed 
at low altitudes, and the second comprising fliglits 
designed to test a new tactic, namely, the use of 
toss bombing for very low-altitude or “masthead” 
attack combined with machine gun and rocket fire 
on the same pass. Another group of tests involved 


the simultaneous tossing of bombs and rockets. 
These three groups of tests used the bomb director 
in a way not originally provided for, so that some 
modification of the standard equipment was neces¬ 
sary in each case. 

Bomb Tossing at Low Altitudes. A set of Mark 1 
Model 0 equipment was used with special modifica¬ 
tions to allow' toss bombing at altitudes below' those 
provided by the standard equipment. Altimeter 
contacts were installed below' 1,390 feet — at 965, 
670, and 465 feet — each contact being 25/36 of the 
next higher contact instead of the standard ratio 
of 5/6. The altitude difference timed by the com¬ 
puter is thus 11/25 of the low'er altitude. An extra 
resistance was added to the integratiDg circuit to 
conform with this change in altitude ratio. This 
change in ratio was necessary since the use of the 
standard value of 5,/6 at very low' altitudes w'ould 
place the altimeter contacts very close to each other; 
the timing interval would in that case be so short 
that any small irregularities in the movement of the 
altimeter catwhisker w'ould result in large errors. 

Prior to the tests proper,-” the gunsight of the 
TBM-IC airplane was calibrated so that the sight 
line Avas on the flight path of the airplane for a dive 
angle of 30 degrees, second altitude 2,000 feet, and 
airspeed of 260 knots. The target for about half the 
Ijombs dropped Avas a hut 20 feet AA'ide and 12 feet 
high at the center, located on a small island, AA'ith 
circular markers of 50- and 100-foot radius. The rest 
of the bombs AA'ere tossed at a toAved sea target con¬ 
sisting of a line of fiA'e spars moA'ing at 8 knots and 
spaced 100 feet apart. 

Eighty-fiA'e ]\Iark 15 Avater-filled l)ombs AA'ere 
dropped singly at three different altitudes and diA'e 
angles. All runs AA'ere made crossw'ind to minimize 
the effect of Avind on the range error. K-24 A'ertical 
photographs Avere taken of the impact points ])y the 
bombing aircraft AA'hen passing directly OA'er the 
target. A summary is given in Table 9. 


Table 9. Summary of low altitude toss bombing tests, ASDevLant, Quonset. 


Avg. Mean point of 


No. 

Avg. 

2nd 

slant 

impact (MPI) 

Mean deviation 

Standard 

of 

dive 

alt. 

range 

(range component) 

about range MPI 

deviation 

bombs 

angle 

(ft) 

(ft) 

(ft) 

(mils) 

(ft) 

(mils) 

(ft) (mils) 

22 

16° 

670 

2,440 

-f 7 

+ 1.0 

42 

5.0 

56 

6.0 

.50 

30° 

2,000 

4,070 

- 8 

- 1.0 

• 68 

8.5 

86 

10.5 

13 

33° 

3,450 

6,420 

- 28 

- 2.5 

66 

5.0 

86 

6.0 


Note. The mil error was measured from slant range at second altitude. It was computed for each bomb impact and averaged to give the value in 
the above table. Mean deviation is the average scatter about the MPI. Standard deviation is root mean square. 








TOSS BOMBING FIELD TESTS 


73 


Toss Bombing Combined with Machine Gun Fire 
and Rocket Fire. Flights were made to test a proposed 
tactic for antisul^marine low-altitude attack which 
entails the use of machine guns, rockets, and bombs 
on the same run.-’®“ The machine guns and rockets 
were fired by “ballistic aiming” and the bombs, by 
tossing ^\ith the Mark 1 bomb director. The tech¬ 
nique consisted of making a well-executed strafing 
run, in the course of which rockets were fired in 
salvo at a predetermined range, after which bombs 
were released automatically by the bomb director 
during the normal pull-up. The sight was not used 
except as an initial guide in aiming machine guns at 
6,000 leet and as a check to keep the flight path 
undeviating during intervals between machine gim 
bursts early in the attack run. A predetermined 
glide angle (15 to 18 degrees) was used. The range 
of rocket firing became a function of temperature 
alone, the other variables being held constant (speed, 
glide angle, angle of attack, launcher line, machine 
gun boresight). The pilot’s principal concern was 
simply to hold the machine gun fire steadily on the 
target. 

The target consisted of a towed line of five spars 
moving at 8 knots. A spacing of 100 feet between 
spars was observed so that photographs from the 
aircraft could be analyzed to give accurate readings 
of the slant range at the instant of rocket firing. 
The center spar represented the gun platform of a 
submarine, 10 feet above the water line. To pass 
through such a point, bullets fired at 15 degrees 
glide should strike 40 feet beyond the spar. Rockets, 
to be lethal, should strike from zero to 70 feet short 
of the spar. The first depth bomb (of a stick of two) 
should strike 70 feet short of the target and the second 
bomb should hit the target. 

Calibration runs were made in order to adjust 
the fall of bombs to the machine gun trajectory. 
The toss bombing ecjuipment was also calibrated 
to produce a hit 70 feet short of the target, with the 
pip of the sight held on the target. The purpose of 
this was to provide for a stick of two depth bombs 
spaced at 70 feet. Allowing 35 feet of underwater 
travel before detonation of the hydrostatic fuse, 
the impact point of number one bomb should be 
70 feet short of the target. The intervalometer was 
calibrated to produce a ground spacing of 70 feet 
between bombs. 

Twenty-four successive runs were made on two 
days. The records were obtained by measurements 
on photographs. Results are given in Table 10. 


Table 10. Results of combined bomb tossing, machine 
gun fire, and rocket fire. 

Plane; TBIVI-IC. Glide angle: 15 to 18 degrees. Range 
at rocket firing: 1,300 to 2,000 feet (approximate). 
Average altimeter contact points (2-pt. Kollsman): 
890/570 ft. 


Desired 

range 

impact 

point 

(ft) 

Actual MPI 
Range Deflection 
(ft) (ft) 

Average 

deviation 

about 

range 

MPI 

(ft) 

Machine gun fire + 40 

4- 32 

4R 

11 

Rocket fire — 40 

- 41 

5L 

24 

First bomb — 70 

- 80 

9L 

37 


Desired spacing between bombs; 70 ft 

Actual average spacing between bombs; 77 ft 
Deviation about the mean (bomb spacing): 17 ft 


Simultaneous Tossing of Bombs and Rockets with 
Mark 1 Model 0 Bomb Director. Tests were con¬ 
ducted at Antisubmarine Development Detach¬ 
ment, Naval Air Station, Quonset, to determine the 
feasibility of simultaneous tossing of bombs and 
rockets with the use of the Mark 1 Model 0 bomb 
director.-^® Pretest flights were made to determine 
the most satisfactory values of the sight setting, the 
bomb MPI setting, and the rocket MPI setting. 
A TBM-3 aircraft was used with a Mark 1 Model 0 
bomb director modified so as to give, for the same 
input time, two different output times during the 
same pull-up, one for rockets and one for bombs. A 
stationary target was used and flight and impact 
data were obtained photographically. Two 3.5-inch 
AR rockets and one water-filled bomb were dropped 
on each run. In order to eliminate as many sources 
of error as possible, only those rounds were analyzed 
which met certain rigid specifications. Only photo¬ 
graphed impacts were considered, and only of those 
runs which were made consecutively from opposite 
headings. 

Results indicated that under conditions of zero 
wind and no target motion, the bomb director would 
toss bombs and rockets simultaneously with approx¬ 
imately the same accuracy as either can be fired 
alone. However, because of the large difference in 
time of flight between bombs and rockets, the 
impact separation became excessive with as little 
as 5 knots wind or target motion. For the same 
reason, the sight-offset method could not be used to 
compensate for the effect of wind on both bombs and 
rockets. 

Tests on Electrical Indicating Altimeter. The 
electrical indicating altimeter was developed (see 










74 


EVALUATION OF THE TOSS TECHNIQUE 


Chapter 8) to provide a more flexible timing device 
than the multiple-contact Kollsman altimeter used 
in ]\Iark 1 directors. It is essentially an aneroid 
altimeter provided uith a potentiometer such that it 
continuously gives a voltage output proportional to 
altitude. This altimeter, together with its associated 
relay circuits, provides that (1) “first-button” 
operation of the computer circuit occurs simul¬ 
taneously with the pressing of the bomb release 
switch, and (2) “second-button” operation auto¬ 
matically follows when the aircraft reaches an alti¬ 
tude which is a preset fraction of the “first-button” 
altitude. Such a device obviously affords the pilot 
greater operational freedom. 

Test on Accuracy of Altitude Ratio of Electrical 
Indicating Altimeter The electrical indicating 
altimeter uas installed in an SB2C-4 airplane at 
NAS, Patuxent. It was set so that “second-button” 
operation would occur at five-sixths of the first 
altitude — altitude at which the bomb release switch 
is pressed. A test was then made to determine how 
accurately and consistently the altimetei' would 
select one-sixth of any slant range. The plane made 
dry dives using different values of the first altitude, 
dive angle and plane s])eed. Motion pictures were 
taken of the instrument panel during dives to furnish 
accurate readings of the altitudes of operation of the 
bomb release switch and the second button. The 
values as read from the film are given in Table 1 lA. 
The variation in the ratio of the second altitude to the 
first altitude was found to be less than 1 per cent. 

Toss Bombing Runs with Electrical Indicating 
Altimeter. The electrical indicating altimeter, with a 
specially constiucted relay box, was installed in an 
SB2C-3 plane together with a standard Mark 1 


Table 11.\. Altitude ratio test of electrical indicating 
altimeter. 


Dive 

No. 

First 

altitude 

(photo) 

(ft) 

Second 

altitude Dive angle Airspeed 
(photo) (observ’d) (observ’d) 
(ft) (degrees) (knots) 

Ratio of 
second 
altitude 
to first 
altitude 

1 

8,980 

7,570 

41 

335 

0.843 

2 

8,970 

7,570 

41 

325 

0.844 

3 

8,960 

7,560 

40 

325 

0.844 

4 

5,960 

4,990 

40 

330 

0.837 

5 

5,930 

4,960 

40 

325 

0.836 

6 

5,975 

5,000 

40 

320 

0.837 

7 

5,960 

4,990 

25 

290 

0.837 

8 

5,965 

4,995 

25 

290 

0.837 

9 

5,950 

5,000 

25 

290 

0.840 

10 

5,980 

5,010 

20 

260 

0.838 

11 

2,985 

2,515 

20 

290 

0.843 

12 

2,995 

2,525 

20 

285 

0.843 

13 

2,980 

2,510 

19 

280 

0.842 


Model 0 bomb director on February 1, 1945. Flights 
were made to determine whether or not the use of 
this altimeter, as compared to the production model 
in use, would give improved accuracy, mainly from 
the point of view of dispersion. The equipment was 
installed so that either type of altimeter could be 
connected to the computer. Toss bombing runs 
were made alternately using the experimental alti¬ 
meter and the standard altimeter. The plane heading, 
altitude points, dive angle, and airspeed were kept 
as constant as possible for each flight. The sight 
was kept fixed on the target on all runs. In view of 
the accuracy with which the electrical indicating 
altimeter gave the timing signals for first- and 
second-button operation at a ratio of 6/5 (see 


Table IIB. Test to compare dispersion of bomb impacts using electrical indicating altimeter and .Mark 1 Model 0 
altimeter. 


.\vg. dispersion about MPI 





Electrical 

Mark 1 




Second 

Dive 

indicating 

Model 0 



Dive 

altitude 

angle 

altimeter 

altimeter 

Plane 


number 

(ft) 

(degrees) 

(ft) 

(ft) 

heading 

Remarks 

1 

4,150 

40 

40 

10 

Upwind 

Winds rough; average velocity, 38 mph. 




(4)* 

(3) 


2 

2,880 

30-35 

80 

180 

Up'vind 

Winds rough; average velocity, 32 mph. 




(4) 

(3) 


3 

2,880 

25-30 

45 

45 

Downwind 

Average wind velocity, 10 mph. 




(8) 

(7) 



* Figures in parentheses show number of bombs dropped. 












TORPEDO TOSSING FIELD TESTS 


75 


Section 5.1.3, “Test on Accuracy of Altitude Ratio 
of Electrical Indicating Altimeter”), this flight test 
did not seek to compare the location of the no-wind 
MPI for both altimeters, but rather the relative 
dispersion of the bomb impacts under approximately 
identical toss bombing conditions. The results are 
summarized in Table IIB grouped according to 
flights made under approximately the same condi¬ 
tions. 

On the basis of the results of the third flight 
shown in Table IIB (the rough and variable winds 
during the first two flights render the dispersion 
data less reliable), it may be concluded that the 
dispersion obtained with the electrical indicating 
altimeter is of the same order of magnitude as that 
obtained with the standard Mark 1 IModel 0 
altimeter. 

This conclusion, although based on a limited amount 
of data, is strengthened by the results of additional 
flights in which 20 boml^s tossed with the use of the 
electrical indicating altimeter, gave an average dis- 
per.sion of 55 feet about the MPI. The second 
altitude was 4,150 feet; the dive angle, 30 to 50 
degrees. 

5-* TORPEDO TOSSING FIELD TESTS 

The efficacy of the Mark 1 Model 0 bomb director 
in launching torpedoes was tested at Gould Island 
Naval Detachment, Naval Air Station, Quonset, 
Rhode Island, during January and February 1945. 
An early model of the toss bombing equipment was 
used in which had been introduced circuit changes 
identical to those incorporated in all later models 
intended for Service use. These changes were based 
on calculations made of the amount by which the 
output time, Tc, must be reduced in order to place a 
torpedo 450 feet short of the tai’get for a toss bomb¬ 
ing maneuver at 1,395 feet second altitude, a glide 
angle of 25 degrees, and 250 knots velocity. Using 
a value of ATc of 3.72 seconds, calculations were 
made of the limiting values of altitude for glide 
angles between 15 and 25 degrees, such that the 
torpedo will fall between 450 and 1,350 feet short of 
the target (see Sections 2.3 and 6.4.10). The purpose 
of the tests at Gould Island was to determine how 
close the agreement was between predicted and actual 
torpedo impacts. 

An SB2C-1 aircraft was used for all flights. 
Torpedoes were Mark 13 Model 2. Prior to torpedo 


tests, flights with Mark 15 bombs were made to 
insure that the airplane sight setting was proper and 
that the equipment was functioning normally. 
Seven torpedoes were tossed, using the normal bomb 
output time; four of these fell within 60 feet of the 
target; the average range error was —100 feet. 
Second altitude was 1,390 feet; glide angle, 20 
degrees. 

Then, using the torpedo setting mentioned above, 
26 torpedoes were tossed, 20 at altitude points 
1,670/1,390 feet, and 6 at 2,000/1,670 feet, dive 
angles 15 to 25 degrees, indicated airspeeds 250 to 
280 knots. No allowance w'as made for wind in 
sighting. Most of the runs were made crosswind. 
Values of impact points were obtained by triangula¬ 
tion. All torpedoes fell within the range predicted 
by theory, as shown by the following summary of 


results. 



Range 

component of 

Second 

Dive 


impact point 

altitude 

angle 

Observed values 

(ft) 

(degrees) 

(ft) 

Theoretical values 

1,395 

18 to 23 

— 870 to — 

435 — 900 to — 450 ft 

(for 15 to 25 de¬ 
grees dive) 

1,670 

16 to 20 

— 900 to - 

705 - 1200 to - 750 

ft (for 15 to 20 de¬ 
grees dive) 


The shift of the impact point with variation in 
glide angle agreed with theoiy, as illustrated by the 
following tabulation of the same results. 




Range component 

Avg. 


Second 

Dive 

of impact point 

devia¬ 

Number 

altitude 

angle 

Range of values Avg. value 

tion 

of tor¬ 

(ft) 

(4eg) 

(ft) (ft) 

(ft) 

pedoes 

1,395 

15-17 

- 870 to - 600 - 715 

110 

4 

18-20 

- 825 to - 4.50 - 670 

85 

10 


21-23 

— 705 to — 435 — 605 

80 

6 

1,670 

16-18 

- 900 to - 720 - 810 

60 

3 

20 

- 780 to - 705 - 745 

30 

3 


The amount of data on hand does not warrant 
more detailed analysis; it is sufficient, how'ever, to 
demonstrate the feasibility of employing the Mark 1 
bomb director for tossing torpedoes. One feature 
wffiich marred the torpedo tests and wiiich was mainly 
responsible for the discontinuance of tests at Gould 
Island was the frequency with wffiich torpedoes sank 
instead of making a normal straight run tow'ard the 
target. Of the total number dropped, about 55 per cent 




76 


EVALUATION OF THE TOSS TECHNIQUE 


had normal runs, 35 per cent sank, and 10 per cent 
had erratic runs. This high incidence of sinkings was 
ascribed to the fact that the target range at Gould 
Island was too shallow for the dive angles used in 
the tests. 

A few tests were made at NAS, Patuxent, just 
before the end of the war, in an SB2C-4 plane, in 
order to check the operation of the torpedo setting 
in the Mark 1 Model 1 bomb director. Miniature 
bombs (ballistic coefficient about 2.3) were dropped 
from a second altitude of 2,880 feet, indicated air¬ 
speed 310 knots. The MPI dial setting was at 0 
and the stick-length dial knob was set at torpedo. 
The results showed good agreement with the expected 
values of the impact points. 

5 3 ROCKET TOSSING FIELD TESTS'^ 

.s.3.1 Equipment and Procedure 

The first rocket tos.sing field tests were made with 
a bomb director Mark 1 Model 0, AN/ASG-IOXN 
which had been adapted to rocket tossing by replac¬ 
ing the second capacitor by one of smaller size, and 
increasing the resistance of the range MPI control 
so as to allow adjustment for rocket and plane speeds. 
This was shortly replaced by another modification 
of the Mark 1 ]Model 0 which transformed it into a 
combination bomb and rocket director. The appro¬ 
priate pull-up time for rockets was obtained bj^ 
inserting a capacitor (adjustable in seven steps) in 
series with the second capacitor at the beginning of 
pull-up. Insertion of the capacitor was accom¬ 
plished through action of a micro-switch operated 
by the iv-block bob when the selector switch was on 
rockets. This latter switch in the bomb position 
restored the circuit to that of the Mark 1 Model 0. 
This combination bomb-rocket director, Mark 1 
IVIodel 0, AN ASG-IOXN, served as the basic test 
equipment for all tests considered in this section. 
Circuit refinements and controls to compensate for 
propellant temperature and for launching with a 
lanyard, added duiing the course of field tests, are 
incorporated in the bomb director Mark 1 Model 2, 
AN/ASG-lOA, which was discussed in Chajiter 3. 
The results cited can, therefore, be taken as indica¬ 
tive of the performance which the Model 2 should give. 

Section 5.3 was written by A. G. Hoyem, formerly of the 
State University of Iowa and now at the Naval Ordnance 
Test Station, Inyokern, California. 


Field tests were conducted at the Naval Air Test 
Stations at Patuxent River, Maryland, and Quonset, 
Rhode Island, and at the Naval Ordnance Test 
Station at Inyokern, California, by Navy personnel 
who were assisted l)y technical advisers supplied by 
Division 4.^*^ Tests were also made at the Army 
Air Base, Dover, Delaware. The testing facilities 
and procedures used at each of these field stations 
are described l)elow. These descriptions are followed 
by a consideration of the tests proper under the 
Sections: 5.3.2 “Preliminary Calibration Tests”; 
5.3.3 “Equipment Evaluation Tests”; 5.3.4 “Special 
Tests.” 

NATS Patuxext River, AIarylaxd 

Approximately 1,400 rounds (mainly 3.5-inch 
aircraft rockets and 5.0-inch high-velocity aircraft 
rockets) were launched with rocket tossing equip¬ 
ment during the course of the test program at NATS, 
Patuxent River, Maryland. TBM, F6F and SB2C 
aircraft were used.^®°466,i8i 

Tests were made to determine the effect of the no¬ 
wind MPI produced by changing slant range, 
release g’s, and airspeed. On account of various 
difficulties, some due to tossing equipment and others 
extraneous, the work done with the SB2C and F6F 
aircraft served mainly to determine the proper A 
factor and sight setting, and to locate the sources 
of the troubles. The Patuxent equipment evaluation 
data included in this report are therefore limited to 
those obtained with a TBM-IC. 

The rocket tossing eciuipment used did not have 
temperature and lanyard controls. Aircraft were 
equipped with Mark 8 gun.sights with Mark 2 
adjustable reflector heads. 

Tossing Procedure. The TBAI and SB2C planes 
carried four rocket pairs per flight, and the F6F, 
three pairs. One pair was tossed on each dive at the 
target, and the pas.ses were alternated between the 
IGO- and 340-degree directions. Impact points were, 
in all cases, scored visually by the pilot (also by the 
observer in the SB2C and TBM planes), and re¬ 
corded in terms of displacement from the target 
along the direction of approach (range), and dis¬ 
placement in the direction perpendicular thereto 
(deflection). As in toss bombing tests, impact points 
which fell short of the target were designated with a 
negative sign, and those which fell long with a 
positive sign. 




ROCKET TOSSING FIELD TESTS 


Method of Evaluating Data. All range impact 
points were expressed in mils based on slant ranges 
measured from the beginning of pull-up. No photo¬ 
graphic records of cockpit instruments were made 
during the tests on MPI variation with slant range 
and airspeed; hence, exact information as to when 
pull-up occurred during these flights was lacking. 
Film records for the tests on the effect of release ^’s 
indicated, however, that as a rule 2 seconds elapsed 
during those flights between second altitude and the 
initiation of pull-up. Since the same pilot made all 
test flights, all slant ranges were accordingly based 
on such a time lapse. Thus, the mil value corre¬ 
sponding to a range impact point of y feet, was 
obtained from the relation 6^ = 1,000 y sin a/R, 
where a is the angle of dive and R (feet) is the slant 
range measured from the point at which pull-up 
was assumed to have been initiated. This slant 
range is given by (/;/sin a) — 1,000, where h is the 
second-altitude point and 1,(K)0 feet is the distance 
the plane would, on the average, cover in the 2 
seconds which elapsed between second altitude and 
the initiation of pull-up. 

The pilot occasionally compensated for deflection 
due to wind by sighting to the right or left of the 
target so the impacts woidd lie within the target 
array. He made no attempt, however, to correct 
for range errors due to wind. 

True airspeeds were determined by a BuAer 
U. S. Nav}*" Aircraft Navigational Computer, Mark 8. 
When the temperature at flight altitude was not 
listed in the original data, the normal lapse rate of 
20 C decrease in temperature per l,000-fo(jt increase 
in altitude was as.sumed. 

Rocket pairs having range separations greater 
than 22 mils were not included, on the basis that 
such separations would be due mainly to causes 
other than normal ammunition dispersion. This 
was statistically permissible since this group 
comprised only 2 per cent of the total number 
tossed. 

Flight Conditions. The pilot, as a rule, held the 
angle of dive to 30 ± 5 degrees, and the indicated 
airspeed at second altitude to 280 ± 10 knots 
(indicated airspeed varied during the test for shift in 
no-wind range MPI wdth true airspeed). The 2,400-, 
5,000-, and 7,200-foot second-altitude points were 
used for tests on the effect of slant range; the 5,000- 
foot second-altitude point, for velocity tests; and 
the 4,200-foot second-altitude point, for the tests 
on the effect of release g’s. 


NATS Quoxset, Rhode Isl.\nd 

Testing at NATS Quonset-®^ was done with a 
TBM-IC and a total of 283 3.5-inch aircraft rockets 
were launched during the test period. Of these 
rounds, 222 were launched as pairs, 40 in groups of 
four, 7 singly, 6 in one sah'o, and 8 in another salvo. 
Mark 8 sights were used, set 2 degrees 12 minutes 
above the thrust line. Launchers were latch-type 
Alark 5 Model 3. The target was the center spar of 
five spars 100 feet apart, which were towed at 7 
knots into or with the wind. 

Tossing Procedure. Passes at the target were made 
crosswind whenever possible to eliminate range- 
wind error. Impacts were photographed from the 
plane as it passed over the target, by means of a 
K-24 camera, mounted vertically. Photographs 
were also made by a photo plane ecpiipped with an 
F-5t) camera. In addition, the pilot and the observer 
who accompanied him made visual estimates of the 
impact points. Flight data were obtained from GSAP 
photographs of the instrument panel. Tests were 
made specifically to observe what effect, if any, the 
tossing distance and the angle of dive had on the 
performance of the equipment. An attempt was also 
made to examine the data thus obtained for the 
effect produced by changes in propellant temperature 
associated with variations in air temperatures dining 
the testing period. 

Method of Evaluating Data. The rounds which 
w'ere analyzed were limited to 159 by rejecting 
those for which: (1) the prescribed test conditions 
were not met, (2) the head or tail wind component 
was in excess of two knots, or (3) no photographic 
impact data were obtained. Ten rounds were 
also excluded because their impact points were 
sufficiently far removed from those of their 
group to indicate that some factor outside the 
equipment, such as bumpy air, abnormal pilot 
error, or di.slocation of the gunsight, had been 
present. 

Impact points were expressed above, except that 
slant range was measured from the second-altitude 
point. Slant range was so measured becau.se the 
pilot generally began pulling up shortlj'' after pass¬ 
ing the second-altitude point, and this point thus 
repre.sented the end of dive toward the point of aim. 
(If slant ranges had been measured from the actual 
release point rather than second altitude, the mil 
values would have been increased between 5 per 
cent and 15 per cent.) 



78 


EVALUATION OF THE TOSS TECHNIQUE 


NOTS, Inyokern, California 

This section includes the results obtained at NOTS, 
Inyokern, up to approximately June 1,1945. i78,i8i,2i9a,b 
Since testing at Inyokern continued after NDRC 
withdrew from the program, and the transfer of 
personnel was gradual, the setting of a boundary 
date for the inclusion of data is somewhat arbitrary 
Approximately 1,700 rockets were tossed during the 
period covered in this report, and of these, 1,550 
were 5.0-inch HVAR and 94 were 11.75-inch All. 
The balance were 3.5-inch AR, 5.0-inch AR, and 
2.25-inch AR (fast). Most of the testing was done 
with F6F-5 and an F4U-1D. Te.sts were also made 
with an F4U-4. 

The Model 0 directors were equipped with tem¬ 
perature and lanyard compensation controls during 
the latter part of the test period. The .sights used 
were Mark 8 gunsights. 

Three target areas, located in the Mojave Desert, 
were used for rocket tossing tests at this base. Each 
target consisted of a OOO-foot scpiare area with a 
bull’s-eye in its center and four camera markers 
each 300 feet from the center and spaced 90 degrees 
apart. Two of these markers were on the flight line 
which was formed by additional markers spaced 
over a distance of several miles on each side of the 
target. An observation station with a hai-p was 
located 1,000 juirds from the target in a direction 
perpendicular to the flight line. The station was in 
charge of the range officer who controlled traffic and 
directed the pilots into the angle of dive prescribed 
for a given test. This limitation on the angle of 
dive was imposed so that the tossing ranges foi- 
consecutive passes during a flight would be essentially 
the same. 

Tossing Procedure. Passes at the target were 
made along the flight line in opposite directions, 
A’S and SN, alternately. Two rockets were tossed 
simultaneously during each pass at the target, and 
their impact points immediately marked with 
numbered stakes. At the completion of the flight, 
the stake iiositions were measured by transit and 
stadia rod and recorded in polar coordinates. Other 
data pertaining to the flight were obtained from the 
pilot’s flight report, loading area data, and the range 
officer’s data. 

A torpedo camera mounted in the starboard wing 
and boresighted parallel to the line of .sight provided 
a picture of the target area from second altitude, 
which could be u.sed in determining the point of aim. 


the slant range, and the angle of dive. Energizing of 
the camera was done by wiring it in parallel with 
the second-altitude light. 

A GSAP gun camera was mounted in the port 
wing of the plane and operated by the bomb release 
switch. It thus provided a sequence of pictures 
which showed the point of aim throughout the 
critical portion of the dive. 

Another GSAP cockpit camera photographed the 
instrument panel so as to record the airspeed meter, 
gr-meter, and altimeter readings, and the operation 
of the first- and second-altitude lights. 

Method of Evaluating Data.^^^ Slant range was 
normally obtained from the torpedo camera film. 
As already stated, the target areas had two on- 
course markers 300 feet on each side of the target 
and two off-course markers similarly located on a 
line perpendicular to the course. If on the torpedo 
camera film the distances between the images of the 
on-course markers is de.signated by dy, and the dis¬ 
tances between the images of the off-course markers 
by dx, then 

i ?2 _ Focal length 

GOO (feet) Jx ’ 

where 7?2 is the distance in feet from the second-alti¬ 
tude point to target. Using this value of R^, the 
slant range is then given liy /G — VT, where V is 
the aircraft velocity at the second-altitude point in 
feet per second and T is the time in seconds from 
.second altitude to the rocket release point. The dive 
angle is also olitained from this film by the relation 
sin a = dy/dj;. If the torpedo camera film was defec¬ 
tive, the slant range was obtained l^y dividing the al¬ 
titude at relea.se by the sine of the angle of dive, using 
values taken from the cockpit camera film. If the 
film from the cockpit camera was not sufficiently 
clear to allow reading of the relea.se altitude, the 
time which elapsed l^etween the second-altitude 
point and release (as shown liy number of frames the 
l)ilot’s indicator light stayed on) was multiplied by 
the true airspeed. This distance was then sub¬ 
tracted from the known range at second altitude to 
give the correct slant range. If this film was entirely 
obscured, the slant range was obtained by sub¬ 
tracting from the second-altitude range an average 
of the distance to release for similar conditions of 
dive angle, speed, range, and pull-up acceleration. 

The range and deflection coordinates (X,Y) of the 
impact points were obtained from the polar coordi¬ 
nates (r,0) by the simple transformations A" = r sin d, 








KOCKKT TOSSING FIELD TESTS 


79 


Y = r cos 6, when the direction of flight is taken 
into consideration. Thus, an impact point to the 
right of the target and beyond it had positive A' and 
y values. The coordinates (A”,!’) in feet w'eie finally 
changed to coordinates ( e^,ey) in mils by the formulas 


ej;(mils) = 


_X (ft)_ 

Slant range (in thousands of feet) ’ 


e^(mils) = 


(ft) sin a 

Slant range (in thousands of feet) 


Army Air Base, Dover, Delaware 

The woi-k at this base was carried on under 
arrangements similar to those for toss bombing 
tests at various Army bases. Tests w'ere conducted 
in a P47-D aircraft equipped with four rocket rails. 
Rockets tossed were 3.5-inch AR. A total of 12-4 
rockets were launched during this period, of which 
84, launched from opposite directions, are analyzed 
in this summary. 

The tossing equipment used was without tem¬ 
perature and lanyai-d compensation controls. The 
sight w as a K-14 fixed gunsight. 

The target was a 50-foot circle, formed by mark¬ 
ers, A\ith a bull’s-eye center consisting of a red 
pyramid approximately 10 feet along its base. The 
area was marshy ground. A road which passed 
through the target in a 115-degree to 295-degree 
direction served as the flight line on all passes. 

Tossing Procedure. Rockets w'ere tossed singly 
on all flights and the passes alternated between 
opposite approaches along the flight line. (A few 
preliminary tosses were made from only one direc¬ 
tion at the recpiest of Army officers to ensure that 
a nearliy farmhouse would not be endangered.) 
Impacts were scored from three observation sta¬ 
tions grouped aroimtl the target, w'hich determined 
the azimuth of each rocket impact point. An auto¬ 
matic device knowm as HARP was used to guide the 
plane into 30-degree dives on all flights. 

Method of Evaluating Data. The azimuth readings 
of impact points w'ere plotted on a chart of the 
range, drawn to scale, and their positions expressed 
in range and deflection coordinates. Slant ranges and 
mil values were determined liy the same methods 
as W'ere used at Patuxent. 


5.3.2 Preliminary Calibration Tests 

Preliminary calibration tests w'ere made to de¬ 
termine the sight setting reipiired to make the plane 
fly a straight course during its dive at a target, and 
to determine the A factor w'hich w'ould produce on- 
target impacts under no-wind conditions. 

The sight setting w'as in most cases determined 
by the theodolite method, as explained in Section 
4.2.1. In some instances, how'ever, poor visibility, 
air roughness, and high-velocity winds prevented 
use of this method. In such cases, recourse w'as made 
to sight setting data given in CIT manuals, 213,214 
the value so chosen checked by determining the 
no-wind AIPI for bomlis and rockets using the 
procedure described in Section 4.2.1. After the 
correct setting had thus been found; the plane w'as 
boresighted, and the angle between the sight line 
and the boresight datum line recorded for future 
convenience in checking oi- resetting the sight. 

The A factor, or rocket calibration (coarse and 
fine) setting, ii-sed in tossing the first rockets of a 
given type, was obtained from theoretical A factor 
curves similar to those shown in Section 7.5 by 
estimating the true airspeed w'hich w'ould be attained 
by the plane during the timing portion of its dive. 
A sufficient number of rockets were then tossed to 
establi.sh a no-wind MPI for the group, using, as 
nearly as possible, the same dive angle and true air¬ 
speed as W'ere employed in calibrating the gunsight. 
Changes in rocket calibration setting necessary to 
bring the no-w'ind MPI on target w'ere then made 
and this corrected setting maintained throughout 
the subseiiuent ecpiipment evaluation and special 
calibration tests. 


5.3.3 Equipment Evaluation Tests 

Included under this heading are the tests which 
w'ere made in investigating the variation in no-wind 
AIPI w'ith tossing distance, angle of dive, plane 
speed, pull-out acceleration, and propellant tem¬ 
perature using the A factors and sight settings 
determined during the preliminary calibration wmrk. 
The results of these tests are summarized in Tables 12 
to 21, inclu.sive, and are grouped according to test 
station. Average values of each variable are given 
for all passes made during a given test. These are 
followed by the mean dispersion of the individual 
values about the average, e.g., 32 ± 2. Columns 






so EVALUATION OF THE TOSS TECHNIQUE 




Table 12. Variation in i\IPI w: 

ith slant range (Patuxent). 



Number 

of 

rockets 

A 

Maximum 

o’^ 

Second 

altitude 

(ft) 

Dive angle Slant range 

(deg). (ft) 

True air¬ 
speed 
(knots) 

Range 

disper¬ 

sion 

(mils) 

No-wind 

range 

MPI 

(mils) 

28 

0.192 

3.0 ±0.1 

2,400 

29 ± 2 

4,300 ± 500 

285 ± 15 

6.6 

+ 3.3 

39 

0.192 

3.1 ± 0.1 

5,000 

33 ± 2 

8,300 ± 600 

305 ± 15 

4.0 

-f 0.6 

29 

0.192 

3.2 ±0.1 

7,200 

32 ± 3 

12,500 ±1,000 

315 ± 5 

5.2 

- 2.8 




(TBM-IC #45473- 

-3.5-in. AR) 







TjVble 13. Variation in 

MPI with true airspeed (Patuxent). 









Range 

No-wind 

Number 


Second 



True air- 

disper- 

range 

of 


Maximum altitude 

Dive angle 

Slant range 

speed 

sion 

MPI 

rockets 

A 

g’a (ft) 

(deg) 

(ft) 

(knots) 

(mils) 

(mils) 

72 

0.192 

2.9 ±0.1 5,000 

29 ± 2 

9,300 ± 700 

275 ± 5 

5.9 

6.8 

66 

0.192 

3.1 ± 0.2 5,000 

29 ± 2 

9,300 ± 800 

305 ± 10 

3.4 

3.0 


(TBM-lC #45473—3.5-in. AR) 


Table 14. Variation in MPI with relea.se g’s (Patuxent). 


Number 

of 

rockets 

A 

^Maximum 

g’s 

Second 

altitude 

(ft) 

Dive angle 
(deg) 

Slant range 
(ft) 

True air¬ 
speed 
(knots) 

Range 

disper¬ 

sion 

(mils) 

No-wind 

range 

MPI 

(mils) 

40 

0.192 

2.0 ± 0.1 

4,200 

30 ± 2 

7,300 ± 

600 

300 ± 10 

6.0 

- 4.7 

26 

0.192 

2.4 ± 0.1 

4,200 

32 ± 3 

7,200 ± 

600 

295 ± 5 

6.5 

-h4.7 

18 

0.192 

2.7 ±0.1 

4,200 

29 ± 2 

7,600 ± 

400 

295 ± 5 

3.6 

+ 5A 


(TBM-IC #45473 — 3.5-in. AR) 


Table 15. Summary of Quonset data. 


Number 

of 

rockets 

.4 

Second 

altitude 

(ft) 

Rocket 

temperature 

(°F) 

Dive 

angle 

(deg) 

Slant 

range 

(ft) 

True air¬ 
speed 
(knots) 

Dispersion 

(mils) 

Range 

No-wind MPI 
(mils) 

19 

.188 

1,390 

32 

17 

5,200 

253 

6.1 

- 1.0 

14 

.188 

1,390 

23 

25 

3,000 

270 

3.1 

3.8 

4 

.188 

1,670 

23 

32 

3,100 

268 

3.5 

0.9 

8 

.188 

2,000 

59 

25 

4,900 

265 

1.0 

2.4 

24 

.188 

2,000 

14 

29 

4,200 

245 

5.9 

2.7 

14 

.188 

2,000 

30 

15 

7,400 

255 

6.6 

- 2.2 

16 

.188 

2,400 

41 

27 

5,100 

260 

5.3 

0.2 

22 

.188 

2,900 

32 

28 

6,300 

240 

7.1 

2.7 

16 

.188 

3,460 

14 

28 

7,500 

2.50 

4.3 

13.5 

10 

.188 

3,460 

64 

26 

7,800 

222 

6.5 

4.5 

4 

.188 

3,460 

61 

19 

10,800 


4.5 

4.5 

8 

.188 

5,000 

28 

26 

11.200 

248 

7.5 

0.8 




(TBM-IC 

— 3.5-in. 

AR) 






































ROCKET TOSSING FIELD TESTS 


81 


Table 16. Variation in MPI with slant range (Inyokern). 


Number 

of 

rockets 

.4 

Release 

g’s 

2 nd 

Alt. 

(ft) 

Rocket 

temp. 

m 

Dive 

angle 

(deg) 

Slant range 
(ft) 

TAS 

(knots) 

Deflection (mils) 
Disp. MPI 

Range (mils) 
Disp. MPI 

24 

0.148 

2.0 ± .2 

2,400 

(F6F-5 f72679 
59 5 33 ± 2 

- 5.00-in. HVAR) 

3,530 ± 280 356 ± 

16 

5.9 

1.7 

5.0 

- 2.7 

36 

0.148 

2.2 ± .3 

5,000 

53 * 8 

34 5 

7,800 ±1,000 

364 ± 

20 

7.0 

- 1.0 

6.8 

- 1.9 

30 

0.148 

2.6 ± .5 

7,200 

52 ± 7 

36 ± 5 

10,750 ± 1,300 

369 ± 

14 

8.0 

4.4 

7.4 

- 3.8 

24 

0.140 


2,400 

(F4U-1D #57181 
57 ± 3 36 ± 1 

- 5.00-in. HVAR) 

3,420 ± 150 320 ± 

11 

9.6 

13.1 

7.1 

- 4.2 

45 

0.140 

3.0 ± .2 

5,000 

64 ± 10 

35 ± 2 

7,890 ± 390 

343 ± 

9 

6.5 

11.2 

7.4 

1.4 

16 

0.140 

3.1 ± .2 

7,200 

52 ± 2 

36 1 

11,400 ± 243 

352 ± 

8 

6.9 

15.1 

5.3 

- 1.8 

16 

0.140 

2.3 

4,200 

77 

45 ± 0 

5,400 ± 210 

338 ± 

8 

8.8 

6.6 

6.9 

11.5 

30 

0.140 (Max.) 4.9 

7,200 

61 

48 ± 5 

8,850 ± 1,000 

365 ± 

19 

8.0 

7.2 

7.8 

2.4 

15 

0.140 (Max.) 4.9 

8,500 

73 

45 ± 3 

10,500 ± 660 

400 ± 

6 

10.3 

10.5 

5.6 

0.9 





Table 

17. Variation in MPI with angle of dive (Inyokern). 




Number 

of 

rockets 

A 

Release 

g’s 

2nd 

alt. 

(ft) 

Rocket Dive 
temp. angle 

(°F) (deg) 

Slant 

range 

(ft) 

TAS 

(knots) 

Deflection 
Disp. MPI 

(mils) (mils) 

Range 

Disp. MPI 
(mils) (mils) 





(F6F-5 #72679- 

- 5.00-in. HVAR) 






0.148 <fe 










43 

0.158 

2.6 ± 0.3 

3,500 

57 ± 4 22 ± 3 

8,230 ± 600 

325 ±13 

11.4 

2.5 

7.4 

- 4.2 

36 

0.148 

2.2 ± 0.2 

5,000 

53 =fc 4 .34 ± 4 

7,800 ± 800 

359 ± 15 

7.0 

- 1.0 

6.7 

- 1.8 

30 

0.148 

2.1 ±0.1 

7,200 

55 ± 10 50 ± 4 

7,740 ± 600 

368 ± 11 

11.4 

4.7 

10.3 

- 0.2 





(F4U-1D #57181 

— 5.00-in. HVAR) 





47 

0.140 

3.0 ± 0.4 

2,900 

68 ± 6 22 ± 2 

7,170 ± 600 

313 ± 15 

9.1 

7.5 

8.1 

- 8.7 

16 

0.140 

3.0 ± 0.2 

5,000 

54 ± 0 35 ± 1 

7,710 ± .500 

347 ± 6 

6.1 

10.9 

6.7 

1.8 

30 

0.140 

4.9 ± 0.3 

7,200 

61 ± 5 48 ± 5 

8,8.50 ± 960 

365 ± 19 

8.0 

7.2 

7.8 

2.4 


Table 18. Variation in MPI with true airspeed (Inyokern). 


Number 

of 

rockets 

A 

Release 

g’^ 

2nd 

alt. 

(ft) 

Rocket 

temp. 

(°F) 

Dive 

angle 

(deg) 

Slant 

range 

(ft) 

TAS 

(knots) 

Deflection (mils) 
Disp. MPI 

Range (mils) 
Disp. MPI 





(F6F-5 

#72679 - 

5.00-in. HVAR) 






7 

0.158 

3.0 ± .6 

5,000 

60 ± 14 

33 ± 2 

8,160 ± 291 

309 ± 

3 

6.5 

- 9.1 

5.1 

7.3 

4 

0.158 


5,000 

72 ± 0 

37 ± 0.5 

7,875 ± 135 

310 ± 

3 

5.7 

2.3 

3.5 

7.0 

12 

0.158 


5,000 

72 ± 0 

34 ± 1 

7,9,50 ± 282 

348 ± 

0 

2.8 

- 1.5 

1.6 

0.1 

4 

0.158 

2.5 ± .5 

5,000 

65 ± 2 

36 ± 2 

6,870 ± 990 

3.58 ± 

22 

5.5 

- 6.5 

3.3 

- 0.3 

18 

0.158 

2.7 ± .6 

5,000 

65 ± 2 

35 ± 2 

7,410 ± 309 

368 ± 

6 

7.6 

- 6.3 

4.9 

0.5 

18 

0.158 

2.0 ± .1 

4,200 

62 ± 2 

35 ± .5 

6,300 ±111 

402 ± 

5 

4.9 

2.3 

7.2 

- 1.4 


Table 19. Variation in MPI with pull-up ^’s (Inj’’okern). 


Number 

of 

rockets 

A 

Release 

g’^ 

2nd 

alt. 

(ft) 

Rocket 

temp. 

(°F) 

Dive 

angle 

(deg) 

Slant 

range TAS 

(ft) (knots) 

Deflection (mils) 
Disp. MPI 

Range (mils) 
Disp. MPI 





(F6F-5 #72679 

— 5.00-in. HVAR) 





18 

0.158 

2.7 ± .6 

5,000 

65 =*= 2 

36 ± 2 

7,410 ± 309 368 ± 6 

7.6 

- 6.3 

4.9 

0.5 

22 

0.158 

2.5 ± .2 

5,000 

58 ± 5 

36 ± 1 

7,680 ± 330 357 ± 10 

9.5 

1.9 

10.9 

- 5.2 



(Max. g’s) 













(F4U-1D #57181 

-5.00-in. HVAR) 





19 

0.140 

2.0 ± .1 

5,000 

59 ± 5 

38 ± 3 

7,533 ± 903 350 ± 17 

8.8 

8.3 

5.7 

- 9.1 

16 

0.140 

3.0 ± .2 

5,000 

54 ± 0 

35 ± 1 

7,710 ± 510 347 ± 6 

6.1 

10.9 

6.7 

1.8 







































82 


EVALUATION OF THE TOSS TECHNIQUE 


Table 20. Variation in MPI shift with propellant temperature (Inyokern). 


Number Second Rocket Dive 

of Release altitude temp. angle Slant range TAS Deflection (mils) Range (mils) 

rockets A g’s (ft) ('’F) (deg) (ft) (knots) Disp. MPI Disp. MPI 


12 0.158 . 5,000 100 ± 3 34:^ 0 7,755 ± 120 367 * 6 6.8 2.0 6.8 6.3 

12 0.158 . 5,000 —2 * 1 34 * 0 8,190 * 240 363 * 2 4.8 —3.5 4.3 —8.8 

(F6F-5 #72679 — 5.00-in. HVAR) 


Table 21. Variation in MPI with slant range (Dover). 


No-wind 


Number 

of 

rockets 

A 

Factor 

Maximum 

g’s 

Second 

altitude 

(ft) 

Dive 

angle 

(deg) 

Slant 

range 

(ft) 

True air¬ 
speed 
(rnph) 

Range 

dispersion 

(mils) 

No-wind 

MPI 

(mils) 

MPI for 

A = 0.240 
(mils) 

31 

0.225 

4.5 * .1 

2,900 

30 * 0 

4,500 * 400 

365 * 5 

9.6 

— 5.4 

- 2.4 

6 

0.225 

5.0 * .2 

5,000 

30 * 0 

9,000 * 0 

375 * 5 

3.6 

— 8.5 

- 2.5 

47 

0.240 

4.0 * .2 

5,000 

30 * 0 

9,000 * 0 

373 * 3 

9.1 

— 1.3 

(- 1.3) 


(P47-D #42-28612 —3.5-in. AR) 


labeled “dispersion” give the average deviation of 
each impact of a group from the center of impact for 
that group. 

Results on the Vakiation in MPI 
WITH Slant Range 

The results olitained in varying the slant range or 
tossing distance are condensed and grouped together 


Table 22. MPI variation with slant range at median 
dive angle (32°). 


Test 

station 

Number of 
rockets 

Slant range 

(ft) 

No-wind MPI 
(mils) 

Patuxent 

(TBM-IC) 

28 

4,300 

3.3 


39 

8,300 

0.6 


29 

12,500 

— 2.8 

Quonset 

(TBM-IC) 

4 

3,100 

0.9 


33 

4,300 

1.0 


16 

5,100 

0.2 


46 

5,300 

1.2 


22 

6,300 

2.7 


30 

8,000 

9.3 


8 

11,250 

— 0.8 

Inyokern 

(F6F-5) 

24 

3,500 

— 2.7 


36 

7,800 

— 1.9 


30 

11,000 

— 3.8 

(F4U-1D) 

24 

3,400 

— 4.2 


45 

7,900 

1.4 


16 

11,400 

— 1.8 

Dover 

(P-47D) 

31 

4,500 

— 2.4 


53 

9,000 

— 1.4 


in Table 22. The analysis of the Quonset data given 
in the table is based on reference 258. Considering 
the results in the order of listing, it is noted that: 


1. The Patuxent data indicate that the no-wind 
range MPI decreases with increase in slant range if 
the differences in true airspeed at the different 
ranges is neglected. The A factor, however, is 
essentially an airspeed correction factor. Also, for 
the 3.5-inch AR, the value used, 0.192, corresponds 
to a 300-knot true airspeed. If account is taken of 
the shifts in MPI which would be caused by the 
differences in airspeeds, which at 300 knots is about 
1 mil decrease in MPI for each 10-knot increase in 
airspeed, the shift in MPI becomes negligible. 

2. The Quonset data show no significant shift in 
MPI. The large range error for the releases at 3,480 
feet second altitude is considered to have been at 
least partially causetl by altimeter error. 

3. The Inyokern F6F data similarly show no shift 
in MPI. The error in the MPFs, averaging almost 
3 mils short of the target, was corrected in the tests 
which followed by increasing the A factor. 

4. The Inyokern F^P data are less conclusiv'e in 
view of the short IMPI and low airspeed for the close 
range tosses. The MPFs are, however, adequately 
on-target for the medium and long ranges. 

5. The Dover data also show no significant shift in 
MPI within the limits of range considered. By 
referring back to Table 21, it will be observed that 
two different values of A were used in acquiring 
these tlata. The IMPFs for the smaller A value were 
corrected so as to correspond to the larger value and 
higher velocity by the formula: 

d0p(mils) = ^^F{y)dA X 1,000. 

21 “ 


This formula is discussed in Section 2.2. 
























KOCKKT TOSSING FIELD TESTS 


83 


It is thus concluded, on the basis of the above 
evidence, that the performance of the equipment in 
tossing rockets is not affected by variations in toss¬ 
ing distance. 

Results ox the Variatiox ix MPI 

WITH THE AxGLE OF DiVE 

The results of the work done under this heading 
at Quonset and at Inyokern in varying the angle of 
dive are condensed in Table 23. 


Table 23. MPI variation with angle of dive. 


Test 

station 

N umber 
of 

rockets 

Average 
angle of dive 
(degrees) 

No-wind MPI 
(mils) 

Quonset 

35 

16 

- 1.4 

(THM-lC) 

61 

24 

4.7 


63 

31 

3.2 

Inyokern 

43 

22 (low-fif pull-up) 

- 4.2 

(F6F-5) 

36 

34 

- 1.8 


30 

50 

- 0.2 

(F4U-1D) 

23 

24 (low-^^ pull-up) 

- 12.7 


23 

20 (high-{/ pull-up) 

- 2.4 


16 

35 

1.8 


30 

48 

2.4 


Conclusions from the foregoing table are: (1) that 
the performance of the equipment in tossing rockets 
is insensitive to the angle of dive for angles between 
30 and 50 degrees; (2) that at dive angles below 
25 degrees, the MPI is short if the pull-up is gentle 
enough so that the maximum g’s attained are less 
than 3.0 (this shortcoming is not tactically signifi¬ 
cant, however, as during combat the pull-up would 
probabh'' be made with high g^s); (3) that the MPI 
will be over the target at dive angles above 45 
degrees and slant ranges below 2,000 yards. 

Results ox the \'ari.atiox ix MPI 
WITH Plaxe Speed 

The results of these tests showing variation of 
]\IPI with plane speed are condensed in Table 24. 

1. 2'he Patuxent data on the effect of changing the 
speed of the plane indicate a definite shift in MPI 
amounting to approximately 1 mil decrea.se in MPI 
for each 10-knot increa.se in speed when the plane 
speed averages 290 knots. 

2. The ivork done at Inyokern with the F6F, which 


involved a greater spread in speed, also indicates a 
similar type of shift. The shift, however, is seen to 
be a function of the plane velocity and is relatively 
insignificant at the higher speeds. This is in agree- 


Table 24. MPI variation with plane speed. 


Test 

station 

Number of 
rockets 

True airspeed 
(knots) 

No-wind MPI 
(mils) 

Patuxent 

72 

275 

6.8 

(TBM-lC) 

66 

305 

3.0 

Inyokern 

11 

310 

7.2 

(F6F-5) 

12 

350 

0.1 


4 

360 

- 0.3 


18 

370 

0.5 


18 

400 

- 1.4 


ment with theory which indicates that the rate of 
shift in MPI should vary inversely as the square 
of the plane velocity (see Section 2.2.10). 

Results ox the Variatiox of MPI 
WITH Pull-Up Acceleratiox 

The results of the tests dealing with the effect of 
varying pull-up acceleration are condensed in 
Table 25. 


Table 25. MPI variation with pull-up acceleration. 


Test 

station 

Number of 
rockets 

Pull-up accel¬ 
eration (g’s) 

No-wind MPI 
(mils) 

Patuxent 

40 

2.0 

- 4.7 

(TBM-IC) 

26 

2.4 

4.7 


18 

2.7 

5.1 

Inyokern 

22 

2.5 (max. q’s) 

- 5.2 

(F6F-5) 

18 

2.7 

0.5 

(F4U-1D) 

19 

2.0 

- 9.1 


16 

3.0 

1.8 


1. The Patuxent data, taken at low dive angles, 
indicate that there is a decided decrease in MPI 
when low release gf’s, less than approximately 2.1, 
are used, whereas there is no apparent shift at higher 
values. 

2. The Inyokern data obtained with each of the 
two planes sub.stantiate the Patuxent findings. No 
data on the number of gr’s at rocket release were 
available for the FGF flights in which a slow rate of 
pull-up was used, due to the fact that the cockpit 


















84 


EVALUATION OF THE TOSS TECHNIQUE 


camera films were obscured. The exceedingly low 
maximum ^-meter reading listed indicates, however, 
that the low-^ type of pull-up was attained. 

It thus follows that, in rocket tossing, best per¬ 
formance is obtained if a sharp pull-up, such as 
would be used in combat, is executed. 

Results on the Vaeiation of MPI 
WITH Propellant Temperature 

The results of the work done at Quonset and 
Inyokern on the effect of jiropellant temperature 
are condensed in Table 2G. 

Table 26. MPI variation vvitli propellant temperature. 


Test 

station 

Number of 
rockets 

Propellant 
temperature (F) 

Xo-wind MPI 
(mils) 

Quonset 

95 

18 

2.4 

(TBM-IC) 

42 

40 

3.0 

3.5-in. All 

22 

59 

3.7 

Inyokern 

12 

-2 

-8.8 

(F6F-5) 

12 

100 

6.3 


5.0-in. HVAR 


1. The Quonset data given here are the result of an 
anal^'sis which was made of the data acquired in the 
tests on slant range and angle of dive, in which 
variation in the temperature of the propellant result¬ 
ing from variations in air temperatures were taken 
into account. No tests were actually made in which 
propellant temperature was the lone variable. Thus, 
though the values given in the summary show no 
appreciable shift in MPI with temperature for the 
3.5-inch AR, the variations due to other factors 
may be masking the effect of the temperature. 

2. 77(6 Inyokern tests, in which 5.0-inch HVAR’s 
were used, were run specifically for the purpose of 
observing the effect of propellant temperature. 
Heating and cooling of the rockets prior to loading 
v as carefully done and a correction, to allow for the 
change in the temperature of the propellant prior 
to firing, Avas applied. The results show that, in 
the case of the 5.0-inch HVAR, the shift in MPI is 
15 to 16 mils when the propellant temperature is 
changed from 0 to 100 F. This shift is about 50 per 
cent greater than the shift produced by CIT mil 
drop tables. 

These results of tests on the effect of temperature 
shoAved the need for the temperature compensation 
control Avhich Avas introduced in the Model 2 equip¬ 


ment. The effectiveness of the compensation Avhich 
Avas added is shoAvn in Table 27 in the Section 5.3.4. 

Oaerall Performance of the Rocket 
Tossing Equipment 

In Figures 7 to 12, are shoAvn the range distribu¬ 
tion of no-Avind impact points for all rockets con¬ 
sidered in the analysis of equipment eA^aluation tests 
conducted at Patuxent, Inyokern, and DoATr. 
The amount of A\'ind error for a given flight, or for a 
group of flights made under similar Avind conditions 
Avas estimated by computing half the difference 
l)etAveen the iMPFs for the tAvo approaches, e.g., the 
NS MPI and the SN MPI. This correction Avas then 
added to or subtracted from the impact point value 
for each rocket comprising the group to determine 
Avhere the rockets Avould liaA'e hit had there been no 
range Avind component or had the pilot made proper 
compensation for Avind error. 

1. The distribution of 332 indiAudual impacts^ 
corrected for AA'ind, of 3.5-inch aircraft rockets 
launched at Patuxent is shoAA'n in Figure 7. This 




50% 




20% 


20% 


1 ■ 


MEDIAN 


5 % 1 

-20 

-10 

t 

TARGET 

10 

20 


NO-WIND IMPACT POINT (MILS) 


Figure 7. Distribution of range errors, corrected for 
wind, of 332 3.5-inch aircraft rockets launciied from 
TBi\I-lC aircraft at Patuxent. .1 factor used was 0.192. 
Height of each lilock is jiroportional to concentration of 
rockets in area. 

graph shoAVs that the 50 per cent and 90 per cent 
regions are centered at 1.8 mils and haA'e a total 
AA'idth of 9.6 mils and 26.0 mils, respectiATl}". Thus,, 
the mean range dispersion AA'ith respect to the center 
of impact for the entire group is approximately 5 
mils. 

2. Figure 8 giA'es a corresponding distribution of 
110 3.5-inch aircraft rockets launched at DoA^er. For 
these, the mean dispersion is seen to be approx¬ 
imately 6.5 mils. Included in this graph are 26 
rockets fired on flights Avhere all passes Avere from 
the same direction. These AA'ere corrected for AA'ind 
error by applying a correction based on the second 
altitude Avind comjionent and the mean flight times 
of the rockets fired on a given flight.. 

















ROCKET TOSSING FIELD TESTS 


85 


3. The Inyokern data for 5.0-inch H\’AR’S are 
similarly shown in Figures 9, 10, 11, and 12. Figures 
10 and 11 give the distribution obtained using 
A factors of 0.148 and 0.158, respectively, to show the 
shift in range with change in A factor. These im¬ 
pacts are combined in Figure 12. Mean dispersions 
are 7 mils for the F4U data and 6.5 mils for the F6F. 



Figure 8. Distribution of range errors of 110 3.5-inch 
aircraft rockets launched from P47-D aircraft at Dover. 
4 factors were 0.240 and 0.225. Height of each block is 
proportional to concentration of rockets in area. 




50% 




20 % 


20 % 


1 5% 


MEDIAN 

♦ 


5% 1 


-I I I ^ I r- 

— 30 —20 —10 TARGET 20 

NO-WINO impact point (MILS) 


Figure 9. Distribution of range errors of 170 5-inch 
high-velocity aircraft rockets launched from an F4U-1-D 
aircraft at Inyokern. 4 factor used was 0.148. Height of 
each block is proportional to concentration of rockets 
in area. 



Figure 10. Distribution of range errors of 164 5-inch 
high-velocity aircraft rockets launched from F6F-5 
aircraft at Inyokern. 4 factor used was 0.148. Height of 
each block is proportional to concentration of rockets in 
the area. 


The actual impact points of the rounds launched 
by the F6F, plotted in a plane perpendicular to the 
line of flight, are shown in Figure 13. When these 
are corrected for wind error, both in deflection and 
range, the pattern is as shown in Figure 14. If the 


impacts are limited to median values of slant range, 
dive angle, and plane speed, the pattern is the one 
given in Figure 5 of Chapter 1. Under the latter 
conditions, the impacts are seen to have a mean 


5% 

-—r 

-30 -20 



50 % 





20 % 


20% 

MEDIAN 

f 


5% 

1 

-10 

TARGET 

1 

10 

NO-WIND 

IMPACT POINT 

(MILS) 


Figure 11. Distribution of range errors of 151 5-inch 
high-velocity aircraft rockets launched from same F6F-5 
aircraft but with 4 factor of 0.158. Compare with 
Figure 10 and note shift in MPI with change in 4 factor. 


I 

TARGET 


NO-WIND IMPACT POINT 


10 

(MILS) 


20 


Figure 12. Distribution of range errors of 315 5-inch 
high-velocity aircraft rockets (Figures 10 and 11 com¬ 
bined). 


dispersion of 5.2 mils in range and 5.45 mils in 
deflection. Figure 15 shows a corresponding impact 
pattern, corrected for wind, for the F4U data. It is 
to be noted that the impacts are centered on the 
target in range but are to the right of it in deflection. 
This would indicate that the pilot who made these 
flights had a consistent tendency to pull to the right 
in executing the pull-up maneuver. 


Special Tests 

The special test classification includes (1) the 
tests made to check the calibration of the tempera¬ 
ture compensation controls, (2) the tests to correct 
the decrease in jNIPI at long range wliich resulted 
from use of temperature compensation, (3) the work 
on launching 11.75-inch AR’s to determine the 
proper lanyard control setting and the effect of dive 
angle and slant range on their MPI, (4) the tests to 
check the theoretical A factor values for 2.25-inch 
AR, 3.5-inch AR, and 5.0-inch AR, and (5) the tests 
to determine the amount of disper.sion associated 





























































86 


EVALUATION OF THE TOSS TECHNIQUE 


with salvo firing. All these tests were conducted at 
Inyokern.^^*- 

Calibration of Temperature Compensation 
Control 

Two types of tests were made in evaluating the 
reciuired temperature control setting: (1) with the 
rockets all at about the same temperature, the con¬ 
trol voltage was changed to find the shift in MPI 
which this change would produce, and (2) the rockets 
were heated or cooled to the extreme allowable 
temperatures and the temperature control set accord¬ 
ing to the theoretical curves given in Chapter 7. 

The results are shown in Table 27. The first test 
showed the shift to be of the proper magnitude (first 


four rocket groups). When compensation for 
temperature was then made (last three groups), 
the ]\IPI was somewhat short at both temperature 
extremes, luit the small number of rockets tossed 
makes the significance of this error doubtful. 

Correction for Decre.xse in MPI at Long 
Ranges When Compensation Is Made for 
Temperature 

A decrease in MPI at long range became apparent 
when a smaller A factor was used in conjunction 
with the temperature controls. This decrease was 
corrected I)}' adding a 7.5-megohm resistor in 
parallel with the rocket calibration condenser. This 
effectively increased pull-up time, particularly for 


Y 



# Impacts of rockets released at slant ranges below 2,000 yards. 

0 Impacts of rockets released at slant ranges of 2,000 to 2,800 yard.s. 
O Impacts of rockets released at slant ranges over 2,800 yards. 


Figure 13. Impact pattern of all 5-inch high-velocity aircraft rockets launched from F6F-5 airplane, plotted in plane 
perpendicular to line of flight. No correction has been made and no attempt was made by pilots to compensate for wind 
error. They always siglited on target. (For distribution of range errors, see Figure 12.) 








ROCKET TOSSING FIELD TESTS 


87 


Table 27. Effect of temperature controls on the MPI (.4 = 0.128). 
(F4U-1D, 5.0-in. HV.\R) 


Number 

Temp. 


Second 

Rocket 

Dive 

Slant 


Deflection 

Range 

of 

control 

Rel. 

altitude 

temp. 

angle 

range 

T.\S 

Disp. 

MPI 

Disp. 

MPI 

rockets 

volts 

g’s 

(ft) 

(°F) 

(deg) 

(yd) 

(knots) 

(mils) 

(mils) 

(mils) 

(mils) 

22 

0 

2.6 ± .4 

5,000 

45 =*= 1 

37 ± 3 

2,500 ± 280 

345 8 

7.6 

8.5 

4.7 

— 2.9 

6 

8 


5,000 

46 ± 0 

36 ± 1 

2,600 190 

348 4 

5.3 

11.3 

2.9 

8.4* 

6 

30 

2.6 ± .3 

5,000 

54 ± 4 

40 4 

2,450 ± 260 

336 ± 9 

3.9 

14.6 

5.8 

9.0* 

16 

30 

3.2 ± .3 

5,000 

42 =±= 2 

38 ± 4 

2,550 ± 240 

344 ± 4 

11.2 

6.4 

4.7 

14.0 

9 

0 

2.8 =t .3 

5,000 

102 ± 0 

35 =*= 1 

2,800 ± 150 

342 7 

9.4 

8.7 

2.3 

— 5.1 

14 

8 


5,000 

63 ± 7 

37 ± 3 

2,800 =t 150 

335 =*= 7 

6.4 

15.3 

6.5 

3.1 

15 

30 

3.0 ± .2 

5,000 

11 ± 0 

35 =*= 1 

2,600 =*= 70 

340 ± 9 

5.1 

12.3 

3.0 

— 2.2 


* Only one pair from one direction. Thus, the fairly high wind which existed makes these data of s.mall value. 



# Impacts of rockets released at slant ranges below 2.000 yards. 

© Impacts of rockets released at slant ranges of 2,000 to 2,800 yards. 

O Impacts of rockets released at slant ranges over 2,000 yards. 

Figure 14. Impact pattern of all (343) 5-inch high-velocity aircraft rockets launched from F6F-5 airplane, plotted in 
plane perpendicular to line of flight. This is pattern which would have resulted if pilot had accurately compensated for 
wind. (For uncorrected impact pattern, see Figure 13.) At all ranges, true airspeed varied from 265 to 410 knots, and 
dive angle from 18 to 58 degrees. 


long-range tosses. The progress of this improvement 
is shown in Table 28. 

LaU-Vching the ILTo-Inch AR 

A series of tests was conducted in which 11.75-inch 
AR’s were launched from F6F-5 and F4U-4 airplanes. 
Of a total of 94 rockets launched, 26 were used to 


find the correct A factor. The rest were used to 
determine the variation in impact point with varia¬ 
tions in flight conditions, e.g., dive angle and range. 

It was intended that, on each flight, two rockets 
would be carried and that they would be launched 
from opposite headings, thereby giving indication of 
wind error and permitting its determination and 
removal. Trouble with defective launchers, and with 





























88 


EVALUATION OF THE TOSS TECHNIQUE 


Table 28. Effect of leakage resistor on impact point (temp, setting = 8 volts). 


(F4U-1D, 5.0-in. HVAR) 


Number 

of 

rockets 

A 

Maximum 

!7’s 

Second 

altitude 

(ft) 

Rocket 

temp. 

(F) 

Dive 

angle 

(deg) 

Slant 

range 

(yd) 

TAS 

(knots) 

Deflection 
Disp. MPI 

(mils) (mils) 

Range 

Disp. MPI 

(mils) (mils) 

16 

0.118 

(Rel.) 

2.5 ± .2 

5,000 

74 =fc 6 

36 ± 0 

2,400 70 

337 ± 5 

7.0 

7.7 

4.5 

2.0 

16 

0.118 

(Rel.) 

2.8 ± .5 

7,200 

69 1 

35 0 

3,550 ± 190 

349 7 

8.1 

11.8 

8.3 

- 7.2 

8*t 

0.100 

4.9 ± .3 

5,000 

44 ± 0 

39 ± 5 

2,400 ± 230 

343 4 

9.0 

8.8 

8.3 

- 2.8 

16*t 

0.118 

4.7 ± .4 

5,000 

71 ± 1 

36 ± 1 

2,380 ± 60 

332 ± 5 

8.9 

16.4 

6.3 

6.4 

13*t 

0.118 

4.8 ± .3 

8,.500 

80 ± 5 

36 ± 3 

3,470 ± 270 

343 ± 17 

10.1 

10.3 

7.1 

13.7 

19*t 

0.103 

4.9 ± .5 

7,200 

72 ± 3 

36 ± 2 

3,570 ± 320 

351 =*= 18 

8.1 

13.9 

8.4 

2.1 


0.118 

5.0 =*= .4 

8,500 

78 ± 0 

39 ± 2 

3,550 ± 240 

363 ± 21 

9.9 

15.4 

4.9 

1.8 

161 

0.128 

4.8 ± .4 

7,200 

73 ± 13 

35 1 

3,740 ± 140 

344 ± 4 

11.0 

8.1 

7.7 

- 3.5 

* The MPI’s have been corrected to correspond to .1 = 0.128, by the formula d6 (mils) = 

g/2V- RdAFM X 

1,000. 





t Leakage resistance = 5.0 megohms. 
X Leakage resistance = 7.5 megohms. 


Y 



Figure 15. Impact pattern, corrected for wind, of all (440) 5-inch high-velocity aircraft rockets launched from F6F-1D 
airplane, Inyokern, plotted in plane perpendicular to line of flight. This is pattern which would have resulted if pilot had 
made perfect compensation for wind error. 


























ROCKET TOSSING FIELD TESTS 


89 


misfires on 16 flights interfered with the determina¬ 
tion of the wind error present, so the single rounds 
which were launched satisfactorily on these 16 flights 
will not be considered in the analysis of the data. 


Table 29. Shift in MPI with dive angle for 11.75-inch 
AR. 


Num- 


Second 

Dive 


Slant 

MPI 

ber of 

Max. 

altitude 

angle 

TAS 

range 

Defl. 

Range 

rockets 

ff’s 

(ft) 

(deg) 

(knots) 

(yd) 

(mils) 

(mils) 

8 

.5.1 

2,000 

20 

320 

1,500 

4.6 

- 0.1 

20 

5.2 

2,900 

36 

341 

1,360 

- 5.4 

1.6 

4 

4.2 

6,000 

51 

411 

2,105 

- 18.0 

4.6 

Table 30. 

Shift 

in MPI with 

range 

(at two 

(live 

angles) for 11.75-inch AR. 





Num- 


Second 

Dive 


Slant 

MPI 

ber of 

Max. 

altitude 

angle 

TAS 

range 

Defl. 

Range 

rockets 

g’s 

(ft) 

(deg) 

(knots) 

(yd) 

(mils) 

(mils) 

20 

5.2 

2,900 

36 

341 

1,360 

- 5.4 

1.6 

10 

4.9 

6,000 

36 

369 

2,725 

5.4 

- 4.6 

8 

4.8 

6,000 

36 

352 

3,155 

- 5.8 

- 4.1 

8 

5.1 

2,000 

20 

320 

1,500 

4.6 

- 0.1 

2 

4.5 

3,500 

20 

353 

3,030 

- 13.7 

- 9.2 


<n 


2 



Figure 16. Impact pattern, uncorrected for wind, of 
11.75-inch aircraft rockets launched from F6F-5 air¬ 
craft, Inyokern, plotted in plane perpendicular to line of 
flight. Test conditions were as follows: 

Slant range 1,030-3,230 yards 
.4 factor 0.215-0.295 (mostly 0.295) 

True airspeed 307-410 knots 
Dive angle 18-52 degrees 

.\verage wind velocity at release altitude 7 knots 

Table 29 shows the shift in no-wind MPI as the 
dive angle increases. It is apparent that some shift 
is present, but the amount of shift is probably 
reduced by the increase in true airspeed as the dive 


angle increases. These data indicate that a small 
increase in MPI can be expected as the dive angle 
increases. 


o 


Y 


o 

20 mils 


O -F6F 
• -F4U 




•o 


x'- 



20 

-H 


MILS 
-X 


O 


C 


-20 


DIRECTION 
OF PASS 


Figure 17. Impact pattern (corrected) of 11.75-inch 
aircraft rockets launched from F6F-5 and F4U-4 aircraft, 
Inyokern. Each point represents impact of two rounds 
launched in same flight from opposite directions, after 
effect of wind has been removed. (Removal of wind 
effect places both rounds at same point.) These impacts 
have also been corrected to correspond to A = 0.295 
and temperature and lanyard setting of 40 volts. 


Table 30 shows the shift in no-wind MPI as the 
range increases. Here, too, the true airspeed was not 
constant and probably had some effect on the MPI, 
but in this instance, the change in airspeed had an 
adverse effect. The data show that there is a slight 
decrease in MPI as the range increases at medium 
dive angles; and that there is a larger decrease in 
MPI as the range increases at low dive angles. This 
effect has been anticipated from previous tests with 
other rockets, and from laboratory tests. Use of a 
7.5-megohm leakage resistance across the rocket 
calibration condenser probably reduced the shift 
which would have otherwise resulted. 

The actual impact pattern of all 11.75-inch AR’s 
launched by the F6F in the above tests is shown in 
Figure 16. Impact points are plotted perpendicular 
to the line of flight and have not been corrected for 
wind. The pattern of the impacts for the 11.75-inch 
AR’s launched by the F4U as well as the F6F, after 
correction was made for wind, is shown in Figure 17. 
The mean dispersion of these rocket groups relative 
to their respective centers of impact under no-wind 
conditions averages 7.2 mils. 



















90 


EVALUATION OF THE TOSS TECHNIQUE 


Check on Theoretical A Factor Values for 
2.25-inch AR, 3.5-inch AR, and 5.0-inch AR 

1. A factor for 2.25-inch AR. A total of 32 
2.25-inch AR’s were launched to find experimentally 
the proper A factor for this type rocket. The 
temperature control was set at 7 volts (from the 
theory) during all tests. The results are as shown in 
Table 31. 

From these data it appears that the proper A factor 
for the 2.25-inch AR (fast) and a true airspeed of 
340 knots is about 0.258. The theoretical A factor, 
which was obtained by extrapolating mil drop 
tables beyond 2,000 yards, is 0.221. In view of the 
data limitation in obtaining this theoretical value, 
it is not surprising that a larger factor is necessary 
in practice. 

2. A factor for 3.5-inch AR. Sixteen 3.5-inch 
AR’S were launched to determine experimentally the 
A factor for this type rocket. The A factor and 
temperature controls w'ere adjusted to the theo¬ 
retical values of 0.216 and 7 volts, respectively, 
corresponding to an expected airspeed of 325 knots. 
The results are shown in Table 32, with a slightly 
larger airspeed than expected. 


The correct A factor to employ for the 3.5-inch AR 
and a true airspeed of 344 knots is 0.232. Had this 
A factor been used instead of 0.216, the MPI would 
have been better still. 

3. A factor for 5.0-inch AR. The results obtained 
in the test to check experimentally the A factor 
required in launching 5.0-inch AR’s are shown in 
Table 33. 

Twenty-four 5.0-inch AR’s were launched. The 
temperature control was set at 8 volts from theory 
for all tests. The A factor was set at 0.250 (the theo¬ 
retical value for 340 knots), but the MPI was short. 
From the above data, it would seem that an A factor 
of about 0.298 would be correct. 


Results of Salvo Firing 

Both the F6F and F4U airplanes were used to 
launch 5.0-inch HVAR in salvo for the purpose of 
checking dispersion. The values obtained for 
ammunition dispersion were: F4U, 6.64 mils in 
deflection, and 7.58 mils in range; F6F, 7.26 mils in 
deflection, and 6.28 mils in range. The complete 
summary is shown in Tallies 34 and 35. 


Table 31. F4U - ID. 


Number 



Rocket 

Second 

Dive 

Slant 


Deflection 

Range 

of 

A 

Rel. 

temp. 

altitude 

angle 

range 

TAS 

Disp. 

MPI 

Disp. 

MPI 

rockets 

factor 


(“F) 

(ft) 

(deg) 

(ycl) 

(knots) 

(mils) 

(mils) 

(mils) 

(mils) 

8 

0.270 

2.9±.2 

__ 

5,000 

36±1 

2,530 ±60 

341 ±9 

6.0 

- 2.3 

4.3 

6.3 

8 

0.260 

2.9±.l 

— 

5,000 

35±1 

2,580 ±60 

339 ±7 

4.5 

1.2 

2.6 

3.9 

16 

0.255 

3.0±.2 

■-- 

6.000 

35 ±1 

2,980 ±280 

347 ±9 

6.6 

6.6 

5.0 

- 4.6 






Table 32. 

F4U - ID. 





Number 



Rocket 

Second 

Dive 

Slant 

Deflection 

Range 

of 

A 

Rel 

temp. 

altitude 

angle 

range TAS 

Disp. 

MPI 

Disp. 

MPI 

rockets 

factor 


(°F) 

(ft) 

(cleg) 

(yd) (knots) 

(mils) 

(mils) 

(mils) 

(mils) 

16 

0.216 

3.0±.2 

68 ±4 

5,000 

36±1 

2,800 ±100 344 ±5 

6.6 

13.7 

5.0 

- 2.2 






Table 33 . 

F4U - ID. 






Number 



Second 

Rocket 

Dive 

Slant 


Deflection 

Range 

of 

A 

Max. 

altitude 

temp. 

angle 

range 

TAS 

Disp. 

MPI 

Disp. 

MPI 

rockets 

factor 

g’s 

(ft) 

(°F) 

(cleg) 

(yd) 

(knots) 

(mils) 

(mils) 

(mils) 

(mils) 

8 

0.250 

4 . 6±.2 

6,000 

60 ±0 

35 ±0 

2,480 ±70 

339±8 

3.9 

11.7 

6.2 

- 16.6 

16 

0.287 

4.5 ±.5 

6,000 

66 ±2 

35±1 

2,400 ±20 

348 ±12 

7.1 

11.6 

6.5 

- 3.7 
























PLANE-TO-PLANE TESTS 


91 






Table 34. Salvo firing summary (F4U). 





Number 




Second Rocket Dive 

Slant 


Deflection 

Range 

of 



Max. 

altitude temp. angle 

range 

TAS 

Disp. 

MPI 

Disp. 

MPI 

rockets 

Course 

.4 

g’s 

(ft) (°F) (deg) 

(yd) 

(knots) 

(mils) 

(mils) 

(mils) 

(mils) 

5 

S-N 

0.128 

4.0 

5,000 72 35 

2,660 

355 

3.7 

3.6 

5.7 

— 5.4 

8 

N-S 

0.128 

5.0 

5,000 80 35 

2,630 

332 

12.8 

6.8 

6.9 

- 1.4 

6 

S-N 

0.128 

4.0 

5,000 63 36 

2,400 

345 

7.4 

- 14.3 

7.4 

24.2 

6 

N-S 

0.128 

4.0 

5,000 78 41 

2,290 

379 

1.4 

- 1.3 

7.3 

26.0 

6 

N-S 

0.128 

4.8 

5,000 82 38 

2,460 

370 

5.3 

7.0 

9.2 

6.5 

5 

S-N 

0.128 

4.0 

5,000 62 38 

2,460 

345 

6.0 

- 3.0 

5.0* 

- 23.8 

* One rocket on this test landed 66.3 mils from the MPI of the other five, and was obviously defective. 

In order to 

give an unbiased view 

this 

rocket was omitted in the computation of MPI and dispersion. 











T.able 35. Results of salvo firing (F6F). 





N umber 




Second Rocket 

Dive Slant 


Deflection 

Range 

of 



Rel. 

altitude temp. 

angle range 

TAS 

Disp. 

MPI 

Disp. 

MPI 

rockets 

Course 

A 

I/’s 

(ft) (°F) 

(deg) (ft) 

(knots) 

(mils) 

(mils) 

rmils) 

(mils) 

4 

N-S 

0.158 

2.3 

5,000 60 

33 8,010 

306 

8.5 

10 

3 

3 

2 

S-N 

0.158 

2.0 

4,170 60 

34 6,360 

335 

6.5 

-21.5 

3 

- 6 

6 

S-N 

0.158 


4,170 50 

32 7,140 

331 

5.8 

1.8 

5.0 

-13.3 

6 

S-N 

0.158 

2.2 

4,170 60 

34 6,480 

345 

4.3 

-18.0 

12.3 

- 7.0 

6 

N-S 

0.158 

2.2 

5,000 - 

40 6,690 

367 

10.5 

- 0.5 

9.7 

21.0 

6 

N-S 

0.158 

2.0 

5,000 - 

50 5,370 

378 

2 

- 7 

3.7 

16.3 

6 

N-S 

0.158 

2.4 

4,170- 

23 9,930 

354 

9.1 

1 

5.2 

- 2.2 

6 

S-N 

0.158 

2.1 

5,000 54 

44 6,030 

372 

7.9 

- 3.2 

4.1 

19.3 

6 

N-S 

0.158 

2.0 

2,000 - 

36 2,940 

374 

10.1 

19.2 

2.8 

28.3 

2 

S-N 

0.158 

2.0 

1,395 -- 

19 3,420 

348 

1.0 

-30.0 

0.5 

-21.5 

4 

S-N 

0.158 

2.0 

1,395 - 

19 3,540 

343 

5.9 

-18.8 

5.8 

-22.3 

6 

S-N 

0.158 

1.6 

2,000 - 

43 2,490 

385 

5.0 

-31.7 

2.7 

- 0.5 


5 4 PLANE-TO-PLANE TESTS 

* The Technique 

Toss bombing was initially proposed as a plane-to- 
plane operation in essentially level-flight bombing. 
The first computers built and tested w'ere for this 
application. The results as shown below, were very 
promising — so promising, in fact, that the tech¬ 
nique, when used with proximity-fuzed bombs, was 
considered too dangerous as a defensive weapon 
against aircraft for further development and risk of 
compromise. Development was stopped in the 
summer of 1943, when it was evident that the Allies 
were assuming air supremacy, and thus an outstand¬ 
ing defensive weapon against bomber formations 
would be of more value to the enemy, if compromised, 
than to the Allies. 

The principle of the toss technique in level, 
plane-to-plane bombing is considerably simplified 
because there is no dive angle correction. The 
yp term, discussed in Chapter 2, becomes unity and the 


computer requires intelligence only as to time to 
target and pull-up acceleration. In application, the 
bombing plane flies a head-on collision course toward 
the target plane and at a predetermined time, pulls 
up from the collision course. The equipment re¬ 
leases the bomb at the appropriate time to intersect 
the collision course at the target.^'”'^®®"^®^ 

Time to target was measured with an ARO radar 
equipment adapted for the purpose by representa¬ 
tives of Division 14, NDRC.^^® •“®® The ARO measured 
range and range rate and was set to initiate the 
computing process when the time to target was 
7 seconds. The acceleration integrator in the 
computer was similar in principle to the Mark 1 
accelerometer. 

Before the start of pull-up and after the 7-second 
point, the integrator circuit charged at a unit 
rate so that the time integral of the acceleration 
was equal to elapsed time. This provided that at any 
time after the start of integration, the part of the 
total integral remaining was proportional to the 
remaining closing time. Pull-up could start any 
time after the 7-second point; delay of pull-out 

















92 


EVALUATION OF THE TOSS TECHNIQUE 



Figure 19. Toss bombing attack on PQ-8 target by B-25 bomber using radar range and 7-second acceleration integrator 
setup. 100-pound inert lVI-30 bombs were equipped with modified T-4 photoelectric fuzes and carried spotting charges. 
Photographs at left show passage of bomb and fuze function in close vicinity of radio-controlled target. Photographs at 
right show another round functioning on passage; at right is mother plane. 

.\ltitude of attack 5,000 feet 
True closing speed 325 mph 

























PLANE-TO-PLANE TESTS 


93 


— 100 FEET 

-75 

-50 

-25 

— PQ-8 

—-25 

— -50 

--75 

Figure 18. Plot of 17 bombs tossed by B-25 bomber 
in terms of minimum vertical passage distance above or 
below PQ-8 radio-controlled target. 

beyond this point did not introduce error. Release 
of the bomb occurred when the time integral of the 


acceleration reached the appropriate value. 


Performance 

Tests of the plane-to-plane tossing technique were 
carried out using a B-25 bomber and a PQ-8 radio- 
controlled target. Closing speeds were about 
400 mph, so that the range was about 4,100 feet 
at the 7-second point. A total of 27 bombs were 
tossed under these conditions. The results, plotted 
in terms of minimum vertical passage distance, are 
shown in Figure 18 for 17 of the bombs on which 
photographic data were obtained. Sixty per cent 
of the bombs were within 50 feet of the target and 
over 90 per cent were within 100 feet. One bomb 
scored a direct hit and another, a grazing hit. 

A few rounds were tried with modified T-4 photo¬ 
electric fuses,'^ carrying spotting charges. Figure 19 
show-s the function of two of these rounds on passage. 


See Volume 3, Division 4. 


>60: 


yx!c 







Chapter 6 

MATHEMATICAL ANALYSIS OF BOMB TOSSING 


‘ SOLUTION OF THE BASIC BOMB 
TOSSING EQUATION 

The xpo Function 

HE i/'o FUNCTION WES defined in Section 2.1.2 a.s 
K + VA'^ — A 2 cos a 

K + Va(A - cos a) 1 + Vl + 2/3 

where K is the time average of A from the beginning 
of pull-up to the release of the bomb, a is the dive 
angle, and 

- gTo sin « A — cos a 
- R -■ 

In Tables 1, 2, 3, and 4 are given values of \}/o for 

A = 2, 3, 4, 5; Tc/V = 0.01, 0.02, 0.03, 0.04, 0.05; 

and a from — 30 to 90 degrees. (Figures in the 
tables are based on a value oi g = 32.2 feet per 
second per second.) Figures 2 and 3 in Chapter 2 
are graphical representations of i/'o based on typical 
values from the tables. The tabulated data, as well 
as Figure 2 of Chapter 2, show that for small 

values of Td V, that is, for short ranges or high 


T.\ble 1. Values of xp^. 
K = 2 


a 

II 

o 

o 

y= 0 02 

Tc 

— = 0.03 

p = 00^ 

s 

d 

Jl 

^1 ^ 

- 30° 

0.886 

0.939 

1.008 

1.110 

1.299 

- 20° 

0.957 

0.990 

1.028 

1.074 

1.128 

- 10° 

0.995 

1.011 

1.027 

1.045 

1.062 

0° 

1.000 

1.000 

1.000 

1.000 

1.000 

10° 

0.968 

0.955 

0.943 

0.932 

0.920 

20° 

0.903 

0.880 

0.859 

0.840 

0.822 

30° 

0.808 

0.778 

0.752 

0.728 

0.708 

40° 

0.691 

0.657 

0.629 

0.605 

0.584 

50° 

0.558 

0.525 

0.498 

0.476 

0.457 

60° 

0.418 

0.388 

0.366 

0.347 

0.332 

70° 

0.275 

0.253 

0.237 

0.224 

0.213 

80° 

0.134 

0.123 

0.114 

0.107 

0.102 

90° 

0.000 

0.000 

0.000 

0.000 

0.000 


airplane velocities, \po does not differ much from cos 
a, while for larger values of TJV the \po function is 

^ Chapter 6 is essentially appendix material to Section 2.1. 
It was prepared by Dr. L. E. Ward of the Naval Ordnance 
Test Station, Inyokern, California, and Dr. Albert London 
of the National Bureau of Standards. 


Table 2. Values of xpo. 
K = 3 


a 

T= o"' 

0.02 

0.03 

y= 0.04 

Tc 

— = 0.05 

- 30° 

0.906 

0.984 

1.095 

1.324 

Imaginary 

- 20° 

0.965 

1.006 

1.067 

1.121 

1.209 

- 10° 

1.002 

1.022 

1.046 

1.070 

1.098 

0° 

1.000 

1.000 

1.000 

1.000 

1.000 

10° 

0.965 

0.949 

0.933 

0.919 

0.905 

20° 

0.901 

0.872 

0.846 

0.824 

0.802 

30° 

0.809 

0.773 

0.742 

0.716 

0.692 

40° 

0.697 

0.658 

0.626 

0.599 

0.576 

50° 

0.568 

0.531 

0.501 

0.477 

0.456 

60° 

0.430 

0.397 

0.373 

0.353 

0.336 

70° 

0.286 

0.262 

0.245 

0.231 

0.219 

80° 

0.141 

0.129 

0.120 

0.113 

0.107 

90° 

0.000 

0.000 

0.000 

0.000 

0.000 




Table 3. 

K 

Walues of xp, 
= 4 

0> 


a 

y- o oi 7= “ 02 

Tc 

— = 0.03 

-r 

o 

d 

II 

T'-o.oo 

- 30° 

0.919 

1.006 

1.149 Imaginary Imaginary 

- 20° 

0.978 

1.031 

1.098 

1.189 

1.338 

- 10° 

1.005 

1.029 

1.055 

1.084 

1.118 

0° 

1.000 

1.000 

1.000 

1.000 

1.000 

10° 

0.964 

0.945 

0.928 

0.912 

0.898 

20° 

0.899 

0.868 

0.840 

0.816 

0.794 

30° 

0.809 

0.770 

0.737 

0.709 

0.685 

40° 

0.698 

0.657 

0.623 

0.595 

0.571 

50° 

0.572 

0.532 

0.501 

0.476 

0.455 

60° 

0.434 

0.401 

0.375 

0.355 

0.338 

70° 

0.290 

0.266 

0.248 

0.234 

0.222 

80° 

0.144 

0.132 

0.122 

0.115 

0.109 

90° 

0.000 

0.000 

0.000 

0.000 

0.000 




Table 4. 

K 

Values of xp, 
= 5 

0* 


a 

0.01 0.02 

Tc 

V ^ 

f.0.04 

II 

o 

d 

- 30° 

0.925 

1.021 

1.185 Imaginary Imaginary 

- 20° 

0.981 

1.039 

1.113 

1.223 

1.408 

- 10° 

1.006 

1.032 

1.060 

1.092 

1.130 

0° 

1.000 

1.000 

1.000 

1.000 

1.000 

10° 

0.963 

0.943 

0.925 

0.909 

0.893 

20° 

0.898 

0.865 

0.836 

0.811 

0.788 

30° 

0.809 

0.768 

0.734 

0.705 

0.680 

40° 

0.699 

0.656 

0.621 

0.593 

0.568 

50° 

0.574 

0.533 

0.501 

0.475 

0.454 

60° 

0.437 

0.402 

0.376 

0.356 

0.338 

70° 

0.293 

0.268 

0.250 

0.235 

0.223 

80° 

0.146 

0.133 

0.124 

0.116 

0.110 

90° 

0.000 

0.000 

0.000 

0.000 

0.000 




























SOLUTION OF THE BASIC BOMB TOSSING EQUATION 


95 


more nearly linear in a. Figure 3 of Chapter 2 shows 
the very small change caused in i/'o by a change in K, 
especially for K > 3. 

The tables and graphs establish the essential 
property of the 4'o function used in the bomb tossing 
equipment, namely, that ypo is chiefly a function of a. 


If equation (4) of Chapter 2 is used in order to 
eliminate dp, the following equation for Tp is ob¬ 
tained 

<#> V - (1 + 2.T)7’,Hana - (1 + <r) r, 

+ T, = 0 (2) 


where 


The i/'i Function 


Referring to equations (13) and (14) in Chapter 2, 
it will be seen that one of the essential steps in 
obtaining the zero-order solution of equation (12), 
Chapter 2 is to replace sin dp by dp and cos dp by 
1 — This results in a restriction on the range 

for w'hich the Model 0 equipment can be used effec¬ 
tively.'^® This restriction is made the more severe by 
omitting the term of degree three in equation (14), 
Chapter 2. 

The restriction of the range due to the use of these 
approximations can be partially removed by using 
in equation (13), Chapter 2, approximations to the 
trigonometric functions w’hich result in an equation 
of degree three for dp. In order to obtain all terms of 
degree three in dp it is necessary to replace sin dp by 
dp — 0pV6, to replace the cos dp which is under the 
radical by 1 — Yd-^ + 0pV24, and the other cos 0p’s 
by 1 — Yid^. The resulting equation of degree 
three in dp comes out to be*’ 


' 1 -f- 3cr 






1 + 


0p3 - 3(1 -f 2a) 0p2 tan a 


M / 


- 6(1 + c)e, + = 0 . ( 1 ) 


/ ¥ + 0- 
0 = ^ /1 + 3(r -h 


672 




1 +• 


Comparison of equation (2) w’ith equation (16), 
Chapter 2, show's that the above equation differs 
from the other only in the possession of a term in 
degree three. Since it is reasonable to expect that 
the solution of equation (2) does not differ greatly 
from the less exact solution it is desirable to write 


Tp=Tpo(l+e), (3) 

w'here Tpo is given by equation (17), Chapter 2 and 
e is a small quantity to be determined. 

When equation (3) is substituted into equation 
(2), the terms containing e to the second and third 
poAvers may be neglected, only terms containing e 
to the first power and those not containing e being 
retained. The resulting equation is a linear equation 
for c, and if it turns out that e is actually small for 
the values of the parameters of importance in bomb 
tossing, the validity of this method for solving 
equation (2) Avill be established. 

The linear equation for e is 

+ 2^) V. 

(1 -h 2 €) tan a — (1 -j- o-) Tpo (1 + e) Tg = 0 


^The ^ function as originally defined, used in the Model 1 
equipment, was primarily concerned with taking into account 
only one additional term in the expansion of cos dp occurring 
as V cos dp in the coordinate of the toss bombing equations. 
The procedure outlined in this chapter gives more accurate 
values of \pi which wdll result from including all the degree- 
three terms. Consequently the \pi for 7’c/F = 0.028, which is the 
design value for Model 1 equipment, will not agree exactly 
with the procedure in Chapter 6. It should also be pointed 
out that the original design for 4'i agrees to within 1 per cent 
or less with corresponding values for rp based on \pe = the 
exact yp function.^* form of presentation given here is 

used because it appears a more logical presentation than the 
actual evolution of values for \p during the development 
program. Most of the values in the tables and graphs in this 
chapter and in Chapter 2 are based on the original \pi function 
rather than the ypi function as derived herein; however the 
differences in the values for the i^i’s can be disregarded. 


or, taking account of the fact that Tpo satisfies 
equation (16), Chapter 2 

^V(I+3€)-^(1 + 2,7)- 

TpO € tan a — (1-f tr) e = 0. (4) 

The solution of equation (4) for e is 

e =-- . (5) 

1 -b O’ T ~ (1 T 2o’)T'potan a S(f>TpQ^ 

If the function \pi is defined by the relation 













^6 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


V'l = ^0 (1 + «), it follows from equation (19), Chap¬ 
ter 2, and equation (3) that 


T = — 

^ p 


K -1- Va:2 _ K 


= 'Pu 


which is an equation of the type for which the bomb 
tossing equipment is designed. 


Table 5. e for different values of Tc/V. 
K = 3 


Dive 

angle 

(a) 

Tc/V O.Ol 

0.02 

0.03 

0.04 

0.05 

0° 

0.0062 

0.0265 

0.0661 

0.1389 

0.2835 

10° 

0.0057 

0.0223 

0.0509 

0.0949 

0.1617 

20° 

0.0048 

0.0185 

0.0392 

0.0676 

0.1049 

30° 

0.0043 

0.0147 

0.0296 

0.0483 

0.0706 

40° 

0.0034 

0.0111 

0.0214 

0.0334 

0.0470 

50° 

0.0025 

0.0078 

0.0144 

0.0217 

0.0296 

60° 

0.0016 

0.0047 

0.0085 

0.0126 

0.0167 

70° 

0.0008 

0.0023 

0.0040 

0.0058 

0.0076 

80° 

0.0002 

0.0005 

0.0011 

0.0015 

0.0020 

90° 

0.0000 

0.0000 

0.0000 

0.0000 

0.0000 


Values of e for /v = 3 are given in Table 5. It will 
be seen that for small dive angles and large values of 
the ratio Tc/V, the values of \f/i are appreciably 
greater than the corresponding values of \po- The 
graph of e based on Table 5 is shown in Figure 1. 


* ^ ^ The i/'o Function 

In Section 6.1.3 an exact solution of equation (13) 
of Chapter 2 is obtained.We find it convenient 
to go back to equations (10) of Chapter 2 which, 
after replacing n by fl can be written 

VTc — I gTf^ sin a = ~ sin dp + IT/cos 9p, 

f.*' (6) 

y2 y2 '' ' 

-^ gTf- cos « = — cos dp — FT/sin dp. 

ng t^g 

where Tf=Tk — Tp is the time-of-fall. Equations 
(6) can be regarded as a pair of simultaneous equa¬ 
tions for the two unknowns, Tf and d. 



Figure 1. e versus a for different values of Tc/V, K 
being constant ( = 3). 


On squaring both members of each of the equations 
of (6) above and adding corresponding members of 
the resulting equations it is found that the angle dp 
drops out, leaving the relation 
^ j,/ _ A ^ co^a ^ gT^\ ^ 

4 M \ (x \ / 

This equation is of degree two in the quantity 
and its solution is given in equation (8). 

Of the four theoretically possible times-of-fall 
obtained by taking the square root of the right-hand 
member of equation (8) the one desired in bomb 
tossing is the smallest positive one [equation (9)]. 


T 2 = ?LTi + ^ + QTcSma ^ j7 cos a gTc sin aV 

L M F > V M F / T '2 J • 

T = E cos a gTc sin a / cos a gTc sin aV g^TV 

^ g ^ M F V ^ “T F~ / 

= — [-yl 1 + (1 + sin a) - 1 + -^(l - sin a) 1. 

g^^ ^ V ^ ^ V - M 


( 8 ) 


(9) 





















SOLUTION OF THE BASIC BOMB TOSSING EQUATION 


97 


It is now desired to solve equation ( 6 ) for dp. 
This can be done in a variety of ways, of which the 
following is adopted here. 


2 1 — cos dp 

If both members of the first of equations (G) be 
multiplied by (1 — cos dp), both members of the 
second of equations ( 6 ) by sin dp, and the resulting 
equations added member by member, the equation 
( 10 ) is obtained. 

{VTc — I gTf sin a) (1 — cos dp) 

— h gTf cos a sin dp = F77(cos dp - 1). (10) 

Expressed in terms of co, equation ( 10 ) is 

VTc — I gTf sin a: — | gT/w cos a + VTj = 0, 
from which it follows that 

VTc + VTf - f gTf sin a 
^ gT/ cos a 

The right-hand member will now be expressed in a 
form free from Tf by making use of equation (9). 
After some algebraic reductions the following formula 
for CO is obtained. 


^ Discussion of the Exact Solution 

It was noted in Section 6.1.3 that four times-of-fall 
can be computed from equation ( 8 ). To each of these 
corresponds a parabolic arc followed by the bomb 
after its release. In Figure 2 are shown these four 
arcs for a typical case; a = 20 degrees, K = 4, 
Tc/V = 0.04. In constructing Figure 2 it was 
assumed that the path of the airplane during pull-up 
is an arc of a circle. The parabolic arcs are tangent 
to the pull-up circle at the four points of release 
Pi, P 2 , P3, Pi- The point at which pull-up is com¬ 
menced is labeled Po- The tangent line at this point 
is the collision course. The parabola tangent at Pi 
is the one used in bomb tossing at present; it has the 
shortest flight time to the target. 

The parabola tangent at P 2 corresponds to a 
larger pull-up angle so that the projectile is lobbed 
onto the target after the fashion of a mortar shell. 
It will be noted that in the case of the lobbing trajec¬ 
tory, small errors in release time or pull-up angle 
will cause large errors at the target. For the trajec¬ 
tory tangent at Pi, which departs relatively little 


gT. 


V r cos a I COS a gTc • X , L . cos q: gTc 

- 1 + - + \ 1 + - -V -— (1 + sm a) + V 1 + - - — (1 - sin a) 

cos aL u ' U, V ' M V 


+ 




1 + (1 

M 1 


sin a) 


, , cos a. qTc . X 

1 + - - — (1 - sin a) 

M F 


( 12 ) 


But 


so that 


tan dp/2 — - , 

CO 


0 p = 2 arc tan — , 


(13) 


and, from equation (4) of Chapter 2 


rr 2F , 1 

Tpe = — arc tan — 
gfl CO 


Further, defining by 


'/'e = 


A' + V A^ - A 


(14) 


it follows that 


, 2F K + 1C~ - K , 1 

\pg = — • - arc tan —. (15) 

gTc n 03 


Equations (12) and (13) provide the exact solution 
of equation (13), Chapter 2 . Equations ( 12 ) and (15) 
provide a means for calculating values of the ypg 
function. 


from the collision course, the impact point will be 
relatively insensitive to small errors in release time. 

The two parabolas P 3 and P 4 correspond to 
negative values of Tf. They would be obtained if 
the airplane were to climb up the collision course 
away from the target, and pull away from the colli¬ 
sion course in a clockwise sense around the circle 
until the release point were reached. This type of 
bombing maneuver is of theoretical interest only. 


Calculation and Graphs of yj/g 

In calculating values of \}/g, equation (12) is used 
to calculate co first. Having co, equation (15) yields 
the value of ypg. It was in this way that Table 6 was 
computed. Entries not given in the table correspond 
to complex values of co; i.e., values of the parameters 
for which 

ols (1 - ,i„ ,) > 1 + . (16). 

F M 



















98 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


For such values it is impossible to obtain a hit, 
however perfect the bomb director mechanism. 

In Figure 3 are shown graphs of ype for various 
values of Tc/V. Above the dashed curve, equation 


(16) is fulfilled. All trajectories used in bomb toss¬ 
ing up to the end of the war correspond to values of 
a and yf/g which fall below this curve. 

Maximum Slant Range. In order to obtain a 



Figure 2. Four theoretically possible bomb trajectories corresponding to typical conditions a = 20 degrees, K = 4. 
Tc/y = 0.04. (Airplane is assumed to follow collision course to Po, then pull up in circular arc, releasing bomb at Pi, 
Pi, Pi, or Pi. Pi is usual release point; P 3 and P 4 correspond to negative pull-up time.) 


T.\ble 6 . Values of ypf, K = 3. 


\ 

\ T' 

a 

0.00 

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

0.10 

0 ° 

1.00000 

1.00793 

1.03398 

1.08753 

1.20513 







10 ° 

0.99215 

0.97241 

0.97645 

0.99720 

1.04311 

1.14843 






20 ° 

0.93341 

0.90626 

0.89324 

0.89156 

0.90348 

0.93189 

0.99706 





30° 

0.85339 

0.81396 

0.78860 

0.77326 

0.76627 

0.76741 

0.77813 

0.80281 

0.85746 



0 

0 

-r 

0.74695 

0.70000 

0.66782 

0.64494 

0.62872 

0.61775 

0.61137 

0.60942 

0.61234 

0.62141 

0.64004 

50° 

0.61896 

0.57029 

0.53656 

0.51155 

0.49240 

0.47736 

0.46551 

0.45621 

0.44909 

0.44392 

0.44059 

0 

0 

0.47481 

0.43057 

0.40019 

0.37753 

0.35977 

0.34539 

0.33348 

0.32346 

0.31492 

0.30760 

0.30127 

70° 

0.32004 

0.28630 

0.26325 

0.24626 

0.23291 

0.22203 

0.21293 

0.20515 

0.19841 

0.19249 

0.18724 

80° 

0.16007 

0.14145 

0.12912 

0.12005 

0.11280 

0.10717 

0.10233 

0.09819 

0.09459 

0.09142 

0.08859 

90° 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 

0.00000 
























SOLUTION OF THE BASIC BOMB TOSSING EQUATION 


99 



Figure 3. i/'e versus a for different values of Tc/V, K being constant ( = 3). When parameter values correspond to 
points above dashed curve A, a hit is impossible, however perfect bomb director mechanism. 

T K 

Curve A corresponds to ■—=- 

* g {K - cos a) (1 - sin a) 



Figure 4. Curves of theoretical maximum attainable ranges in toss bombing at different aircraft velocities. K = 3. 
(For theory see text, Section 6.1.5.) 











100 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


formula for the maximum slant range, S^, it is only- 
necessary to make Tc in equation (16) as large as 
possible without having this relation fulfilled; that is 

^ cos q:\ 

_M / 

<7 (1 — sin a) 




Figure 5. 9 pm and (f)m versus a. 9 pm is pull-up angle 
corresponding to theoretical maximum range of Figure 4. 


Since slant range is given by 5 = VTc, it follows that 



Figure 4, based on equation (17), provides a 
graphical means for determining the maximum slant 
range for the case K = 3. For instance, with K = 3, 
a = 20 degrees, V = 300 knots. Figure 4 shows 
that Sfn = 17,600 feet. This is, of course, the 
theoretical maximum slant range; in practice, 
instrumental errors, air resistance, etc., operate to 
reduce this maximum materially. 

It is well known that for a gun firing down a hill 
having a declination a with respect to the horizontal, 
the maximum slant range is obtained if the gun is 
elevated at the angle (45 — q:/ 2) degrees. In Figure 
5 is shown the graph of the pnll-up angle 9p^ 
against dive angle which, for K = 3, secures the 
maximum range. The actual firing angle 9p,p — a 
is somewhat greater than (45 — a '2) degrees 
because in bomb tossing the maximum range is 
referred to the beginning of pull-up, while in the 


case of firing from a fixed gun the range is referred 
to the point of release. 


6 2 PULL-UP ACCELERATION 

6.2.1 YUg Four Types of Acceleration 

In Section 6.1 no special form was assumed for 
the pull-up acceleration. Observed pull-up accelera¬ 
tions are of four types as illustrated in Figure^6. 






TYPE 3 TYPE 4 

Figure G. Four main modes of variation of pull-up 
acceleration with time. (Based on photographic records 
of accelerometer response.) 


Some idea of the relative frequency of occurrence 
of each of these types is given in Table 7.^-* 

Tabi.e 7. Summary of acceleration types experienced 
during pull-up. 

Total 


number of Percentage of total 


Airplane 

records 

Type 1 

Type 2 

Type 3 

Type 4 

SB2C 

36 

33 

22 

45 

0 

tb:^i 

28 

18 

54 

14 

14 

Total 

64 Average 27 

36 

31 

6 


The type 4 curves which have been observed are 
usually of such a nature that the}'' may be reason¬ 
ably well approximated by a type 2 curve. For 
this reason, and because pull-up acceleration of type 






















FAKTICULAK I‘ULL-UP ACCELERATION 


101 


2 is most frequent, the theory will be developed 
for that type. (Type 3 is considered in reference 34.) 
^^^lile it is true that the exact solution in Section 
6.1.3 applies in the case to bo considered here, it is 
worth while to develop this case independently since 
a different function of K than the one in equation (15) 
is indicated as possibly desirable. (Also, a different 
\p function will result, depending on the type of the 
acceleration function.®3) 


The Condition for a Hit 


The number K is assumed to be given by the pair 
of expressions 

K = pt + cos a 0 <t < Ti 

K — Ki = pTi + cos q: Ti 


where p is the constant rate of increase of K during 
the first phase of pull-up. It follows that 


P = pt 

M = Ml = pTi 


0 <t < Ti 

Tr<t. 


(18) 


From equation (2), Chapter 2, and equation (18), 
the angle 6 is found to be given by 


where 


2F 

pgT 

V 




(19) 


0 < f < Ti, Ti <t. 

It then follow^s that the components of velocity are 


X = F cos , y = F sin — 0 < i < Ti, 
2F ’ 2F - - > 

( 20 ) 


and 


a: = F cos 


-?) 


(-’'•'"'-f'O-?) 


Ti < t. 


( 21 ) 


It is necessary to integrate these components of 
velocity in order to get the coordinates during pull- 
up. In order to carry out the integration by means 
of elementary functions the approximations 


cos 0=1— 6^/2; sin 6 = 6 
are made for 0 ^ t ^ Ti. No approximations are 


necessary for t = Ti. In this w^ay the equations 
(22) and (23) are obtained. 


X Vt - 


40T" ’ 


y = 


pgt^ 


0 <t < Ti. 


( 22 ) 


a:= FTi- 


40F pgT, 2F 2F ’ 


Ti < t. (23) 


y 


pgT,^ , 2F2 . pgTrit - T) . pgT,t 
—^F— • 


From equation (9), Chapter 2, and by elimination 
of the time-of-fall Tf = Th — Tp, the condition for a 
hit is obtained in the form 


yrj, _ Xp cos a 4- yp sin a Xp cos a + yp sin a 
cos a g cos^ a 


(yp + ^Vp^ + 2yyp cos a). (24) 


Expressions for Xp, i/p, Xp, and ijp may now be placed 
in equation (24) which then becomes an equation 
for the determination of Tp. 

The case Tp = Ti. If the bomb is released during 
the phase of pull-up in which the acceleration is 
increasing, equations (20) and (22) are used to get 
the components of velocity and the coordinates at 
release. At the same time the quantity p may be 
eliminated by use of the relation pTp = Kp — cos a, 
where Kp is the value of K at release, so that 


Xp 

yp 


= Fcos——^ ~ 

2F ~ 8F 

= V sin ^ yTp (Kp - cos a) 

2V ~ 2 


Xp = FFp 


p-g-Tp^ 

40 F 


FFp 


40F 


(Kp — cosay, 


^ pgTp^ ^ gTp^Kp - cos a) 
6 G 


When these expressions are placed in (24), an 
equation of degree three in Tp results. Omitting the 
term in Tp^, this equation is 


Kp — cos a 4- V (Kp — cos a) (Kp ^ cos a) X 
y (Kp — cos a) tan a 
2F 

+ [Kp -f cos a + V(A'p — cos a)(Kp -j- ^ cos a)] 7'p 
— 2Tc cos a = 0. (25) 

If, for brevity, equation (25) is regarded as 
ATp^-\- 0Tp- 27’, cos a = 0, 






















102 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


the solution for Tp can be put into the form 
„ 4 Tc cos a 


|3 + V)32 + SAT, cos a 


n = 


2 T, cos a 


Kp + cos a + V {Kp — cos a) {Kp + f cos a) 

2 


X 


1 + V 1+ 2/3' 


(26) 


where 


4A7\cosq! „ 7"c/t- n • 

/3 =- ^ -= 2g ~ {Kp — cos a) sin a X 


Kp — \ cos a + V {Kp — cos a) {Kp + | cos a) 
[Kp + cos a + V Kp — cos a) {Kp + cos a)]^ 
The relation between Kp and K is given by 

K = -- f ^ Kdt = + cos a = I (Kp + cos a) 

TpJo 2 

or Kp = 2K — cos a. 

On replacing Kp by 2K — cos a, a formula is obtained 
which closely resembles that for TpQ in equation (18) 
of Chapter 2. The slight differences are due to the 
somewhat different methods used for the approxi¬ 
mate computation of the integrals for x and y 
from the expressions for x and y. 

It is easily verified, using the relation 

K = pt -\- cos a, 

that 

2p f ^(k A K yj —co^ \ ^ {Kp— cos a) X 

JO \ ' K 4- g cos a ' 

[Kp -t” cos a + V (Kp — cos a) {Kp -f I cos a)]- (2") 

By virtue of equation (27) it is possible to write 
equation (26) in the form 




1 + Vl + 2 g - [''’■{k + kJ dl. 

2 cos a Jo \ \ _|_ i ^Qg 


(28) 


This equation suggests the use of 


K + K yj 


K — cos a 
K -f ^ cos a ’ 


where a is a mean value of the dive angles expected 
to be used, instead of K + V K^ — K as the acceler¬ 


ometer function, with, of course, \p defined as follows: 

I K — cosa 

, 2 cos a I ' K 4- ^ cos a 

^ ^— . 

1 -f V 1 4- 2/3 1 K — cos a 

^ K 4- 3 cos a 


THEORY OF INSTRUMENTAL DESIGN 


Selection of Tc/V for xjj 


In designing the gyro potentiometer card it is 
necessary to select a specific set of values of the 
\p function, that is, the set of values corresponding 
to a particular value of Tc/V. The particular value 
of Tc/V selected should correspond to a mean of the 
values of range and velocity at which the bomb 
director is to be used, taking into account the fact 
that the .tendency is to conduct bomb tossing 
maneuvers at approximately the maximum opera¬ 
tional range. 

Figure 11 in Chapter 2 shows the theoretical 
maximum ranges at which a bomb released by the 
Model 0 bomb director would fall within 100 feet of 
the target. When the loci of points for constant 
Tc/V values were superposed on this curve, it was 
found that the locus for Tc/V = 0.028 represented a 
good average for the operational conditions expected. 
Accordingly this value was chosen for the \pi design 
of the Model 1. 

The theoretical maximum ranges for the Model 1 
are shown in Figure 7. By comparison with Figure 
11, Chapter 2, it may be seen that these ranges are 
33 to 60 per cent greater than for the Model 0.^^ 

In Figure 8 are shown graphs of \f/i against a for 
Tc/V = 0.014, 0.028, and 0.042. The ^ card is 
designed so that the effective instrumental \p fits 
the theoretical \p for Tc/V = 0.028 between a = 20 
degrees and a = 70 degrees. Below 20 degrees the 
theoretical yp functions separate widely. For this 
reason, the design^ is the one indicated by the dotted 
line from a = 10 degrees to a = 20 degrees, and is 
taken as 1.0 from a = 0 degrees to a = 10 degrees.®’’ 

It is necessary, then, to design a potential divider 
which, by equation (25), will provide a voltage 
given by 


1 - exp [- TcP{a)/2Qi\ 
1 - exp (- r,/20) 


(29) 
































THEORY OF INSTRUMENTAL DESIGN 


103 


Values of Va obtained from equation (29) using for 
^{a) the values of \f/i corresponding to Tc/V = 0.028 
and V = 500 feet/second, and based on Vo = 150 
volts, are shown in Table 8. 


Table 8. \p card voltages of various dive angles. 


Dive angle 

0° 

10“ 

O 

O 

CO 

o 

o 

O 

O 

50“ 

60° 

75“ 


1.0 

1.0 

0.88 

0.77 

0.64 

0.51 

0.38 

0.18 

Va (volts) 

150 

150 

137 

124 

108 

90 

70 

36 

t^o = 150 volts 

To = 

■ 14 seconds 

V = 

500 ft/sec Tc 

/V = 

0.028 


6.3.2 Variations from Selected Tc/V 

The voltages given in Table 8 are those required 
from the gyro card in order to obtain an instrumental 
\{/ equal to the design rp for Tc/V = 0.028. It is 
necessary to consider how to correct these values 
when Tc/V has other values. The rate at which 
charge accumulates on a capacitor decreases as the 
accumulated charge becomes greater. This means 
that for larger values of Tc, less charge will accumu¬ 
late than would be the case if the rate of accumulat¬ 
ing charge were constant. Consequently, for large 


60* 



a. 

3 

I 


3 

Q. 


UJ 

UJ 

u. 


ilJ 

o 

3 


Figure 7. Curves of maximum allowable ranges (for different aircraft velocities) corresponding to horizontal errors of 
less than 100 feet for bomb director Mark 1 Model 1 (\pi function). 















104 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


values of Tc the effective is smaller, and for smaller 
values of Tc it is larger. Thus, this nonlinear charg¬ 
ing characteristic automatically provides some com¬ 
pensation for the variation of Tc/V from 0.028. 



Figure 8. versus a for Tc/V = 0.014, 0.028, and 
0.042, K being constant (= 3). Solid lines are theoretical 
values; points (Q, X, A) are corresponding instrumental 
values obtained when 4'i card is designed to fit for Tc/V 
= 0.028 and F = 500 feet/second. Dashed lines are 
explained in text. 


Va in accordance with variations in V. The voltage 
required at a = 40 degrees for different velocities is 
shown in Table 9. 

These values are found from (29) by taking (/'(a) = 
0.643, Tc = 0.0287, vq = 150 and calculating v„ for 
various values of V. Knowing these values of it is 
pos.sible to calculate the effective xp for the different 
velocities. Figure 9 shows the results of such cal- 


0.7 


0.6 

0,5 


0.4 


0.3 

0.2 



800 


FT, 


'sec 

THEORETICAL 

SOOFTxsec 


0.1 - 

o|_I_ \ _I_I_I_1_I- 

0 10 20 30 40 50 60 70 

c<( DEGREES) 

Figure 9. Curves showing extent of variation of in¬ 
strumental \pi functions between extremes of velocity, 
when xpi card is designed to fit theoretical (dashed) 
curve at velocity 500 feet/second, Tc/V held constant 
at 0.028. 


Table 9. \p card voltage variation with speed. 


Velocity (ft/sec) 

Tc(sec) for Tc/V = 0.028 

(volts) 

300 

8.4 

103.6 

400 

11.2 

105.8 

500 

14.0 

108.0 

600 

16.8 

110.2 

700 

19.6 

112.3 

800 

22.4 

114.3 


If V deviates from 500 feet/second, it is still 
desired that the \p provided by the instrument agree 
with the theoretical \p for Tc/V = 0.028 and over a 
considerable range of dive angle. In order to secure 
this adjustment, means must be provided to change 


dilations for the extreme cases of V = 300 feet/ 
second and 800 feet/.second. For easy comparison the 
values of \p for V = 500 feet/second are included.®^ 

6.3.3 Physical Dimensions of xp Card 

In Figure 10 the voltage as given in Table 9 is 
plotted against a. The curve thus obtained is approx¬ 
imated to by three line segments as shown, which 
correspond to the functional values of the curve 
within 3^ per cent up to 70 degrees. It is therefore 
possible to make a potentiometer card with three 
different linear sections which will give an excellent 
fit. From the same figure the volts per degree re¬ 
quired for each of the three linear resistance strips 
can be determined. See Figure 11 for dimensions. 












ERRORS AND INSTRUMENTAL ADJUSTMENTS 


105 



Figure 10. Curve of voltage Fa versus a. Instrumen- 
tally this curve is approximated by three straight line 
segments joining consecutive points A, B, C, and D. 



TO* 


52* 


0* 


BASIC DIMENSIONS FOR 3-STEP ip, CARD DESIGN 

Figure 11. Basic dimensions for three-step xpi card 
design. 


Stick-Length Offset 


The expression ATc can be obtained from equa¬ 
tion (20) of Chapter 2 for vi and equation (22) of 
Chapter 2 written in the form 

r _ i *“] 

V 2 = (vo - E) \ I - e "J (30) 

together with the condition for firing of the thyratron, 
V 2 = Vi — E, and the relation 

(n - AT,) = 10 ^ . (31) 

Jo R 

The result of eliminating the integral between the 
tAvo above equations can be written 

(n - ^TJ) lAi = - 20 hi fl-^ 

\ Vo — E 


Replacing in this equation by t’l — E and solving 
for ITc yields the formula 


ITc = Tc - — In^^ -(^^) 

1 - (Vi/Vq) 


(32) 


Let STc represent the value of ATc corresponding 
to E on a bench test for AA'hich a = 0 degree, xpi = I, 
and I'a = I’o- It then follows that 

aT\= - 20 In (33) 


Since E« t>o, this relation shoAvs that ATc is nearly 
proportional to E. By means of equation (33) and 
ecpiation (20), Chapter 2, equation (32) can be put 
into the form 


AT. 


at; 

'Pi 


+ n + — In 

'pi 



Cad 

Vo 



Figures 12A and 12B exhibit graphically the 
relation (34) betAveen AT. and A7’. for the values of 
the parameters indicated. 


As mentioned in Section 2.1.G, the stick-length 
offset is an adjustment by means of Avhich the range 
can be reduced liy an amount corresponding to a 
shortening of the input time T. by the amount A7’.. 
In the Model 0 bomb director this Avas done by 
biasing both capacitors Ci and C 2 by a \mltagc E 
selected by a setting of the stick-length offset dial. 
In the Model 1 equipment the circuit is arranged so 
that the second capacitor only is biased. This results 
in the decrease AT. for the Alodel 0 director, being 
approximately tAvice as great as that obtained from 
the Model 1 circuit for the same biasing voltage. 
In the folloAving discussion the Model 1 etiuipment, 
only, is considered. 


0 ^ ERRORS AND INSTRUMENTAL 
ADJUSTAIENTS 

^ ^' Types of Error 

For con\"enience, the problems to be studied in 
Section G.4.1 are classified under four main headings, 
as folloAA's: 

1. Errors in the ip function. 

a. Range limitations due to the use of \po. 

b. Range limitations due to the use of \pi. 

c. Dive angle error. 






























106 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


2. Error in the pull-up time — range limitations 
corresponding to the degree of accuracy of the 
determination of Tp. 

3. Errors in Tc. 

a. Altimeter error. 

b. Intervalometer characteristics. 

c. MPI adjustment. 

d. Torpedo tossing. 

4. Error due to misalignment of sight. 


so that 


tanV = - r /) CO.S 

g(T,' - Tp') sin« + i/ 


(37) 


where 7\' is the time along the trajectory from P' to 
IP. In obtaining equation (37) from (36) the sign 
of the right-hand member was changed because 
dh is the supplement of the angle given by (36). 

The quantity T/ = 7\' — Tp is now obtained 



Figure 12A. Relation between “stick offset” setting (ATc) and actual resulting offset (ATc) for different values of 
Tc/V; a = 40 degrees, K = 3, V = 500 feet/second. Dashed curve is inserted as aid in comparing magnitudes of ATc 
and ATc. 


The Basic Equation 


Equation (27) of Chapter 2, repeated here as 
equation (35), is basic in problems concerned with 
errors in bomb tossing. 


_5_ ^ rA7; 
sin dh sin (a + 0/,') 


(35) 


The meanings of the symbols in equation (35) were 
previously defined with respect to Figure 10 of 
Chapter 2. Essentially the horizontal range error 5 
is expressed in terms of an error in release time ATp. 

It is necessary to obtain an expression for d^'. 
A starting point is equation (8) of Chapter 2, to¬ 
gether with the corresponding equations for the 
components of velocity. If Tp is the pull-up time 
from 0 to P', and 6 the angle between a tangent line 
to the trajectory P'lPK' and the collision course 
(refer to Figure 10, Chapter 2), then 


tan 6 


y_ ^ ilp - git - tp) cos g 
X ip -\- g{t — ip) sin a ’ 


(36) 



Figure 12B. Actual offset {ATc), as function of a, 
corresponding to different instrumental “stick offset” 
settings (ATc); Tc/V = 0.028, K = 3, V = 500 feet/ 
second. 

















ERRORS AND INSTRUMENTAL ADJUSTMENTS 


107 


from equation (11) of Chapter 2 as 

V 


T/ = 


g cos a 


X 


l^sin dp ' yjs 


• ^ „ f I 2 cos a , , 

sin2 dp + -_— (1 - cos dp) 

n 


Finally, if cot dp is replaced by I/dp', we have 

■yji 




COS a 


(38) y^rp — 


This equation, and the relations Xp' = V cos dp, 
ijp = V sin dp, bring equation (37) to the form 


sin a + 0 


, siiF a + Vl + (1/ ji) cos a 


. (44) 


-^si 


sin^ dp + cos a ^ 


tan dJ = 


cos dp + tan 


aj^sin dp + 


sin^ dp + 2 cos a 


1 - 


(39) 


For small dp this is approximated to by 

dp ' \j 


tan dk = 


1 H-cos a 

M 


1 4“ dp' tan 


« yj 


Equation (35) can be written 
5 1 


1 + — cos a 
M 


A variant of equation (44) using the quantity /3 
will be useful in Section 6.4.3. By the use of equa- 
tions (4) and (17) of Chapter 2, the relation 

2l3 cot a 


1 + Vl + 2|8 


1 + 




= V 


VATc sin a cot d/,' + cos a’ 


(41) 


fi + cos a 

is obtained, and thus equation (44) becomes 


VAT^ 


1 + sin^ a 


1 +Vl + 2/3 
2/3 


1 ^ (^/^ + 2ft + 

1 P 

' /I 4- cos a ' ^ 

M 4“ cos a' 


(45) 


and it is a simple matter to replace cot d^ by its 
value from equation (39). The resulting equation 
can be put into the form 




^jl + 


2 cos a 
m( 1 + cos dp') 


sin a (tan a + cot dp') + —^— W 
cos a y 


to which a good approximation is 

5 c- 

VATc ~ 

L , 1 

V 1 4-cos a 

M 


1 + 


2 cos a 
ii(i + cos dp) 
(42) 


sin a (tan a 4* cot dp) 4“ 


4 


1 4—cos a 
A 


Range Limitations 
from the Use of 

For the discussion of range limitations due to the 
use of ^ 0 , or of range errors due to errors in the meas¬ 
urement of yp, a formula for 5 in terms of ype and ypQ, 
or in terms of the error in yp is needed. Equation (45) 
can be used to obtain such a formula. 

In the first place, if *S = VTc'is the slant range OH, 
then 

^ _ 8 ATc ATp 

S ~ VATc ' ATp' 'Tp 
Of the four factors comprising the right-hand 
member, the first is given by equation (45), the 
second and fourth are to be taken from the equations 
of Section 2.1.2, and the third will be retained in its 
present form. 

From equation (16) of Chapter 2, in which ju is 
assumed to change by an amount small enough to be 
ignored, it is found that 

1 4 - 2(7 


(46) 


dTc = 


gjiTpo tan a 4~ (1 4- o-) dTpo, 


(43) 


V 



















































108 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


as well as 



II . 1 + 2(r _rn . 

1 + O’ + -—I 


2V 


It follows that 




dTpQ Tc 1 I _ I f "h 2(r ^ _ 


1 + (T + 


27 


gjiTpo tan a 


= 2 - (\ + a) 

Tc 


(47) 


On replacing Tpo in the right-hand member by its 
value from equation (17) of Chapter 2, and express¬ 
ing the result in terms of /3, we obtain 

^ ^ 2 Vl + 2/3 

dT^ ' T, 1 + Vl + 23 • ‘ ^ 

Substituting equations (48) and (45) into (46) 
results in 


from 0.015 to 0.05 at intervals of 0.005 were plotted, 
and each labeled with the value of Tc/V to which it 
corresponded. Now S = {Tc/V)V'. Hence for a 
constant V, eight values of *S can be calculated, one 
for each Tc/V curve, for all eight of which Fhas the 
same value. These eight points are then connected. 
Repetitions of this procedure give the curves of 
constant V in Figure 11 of Chapter 2. 


^ Range Limitations from 

the Use of 

Equation (49) can be used to obtain curves for the 
Model 1 director {\pi function) corresponding to 
those in Figure 11 of Chapter 2 but for the Model 0 
bomb director. Such a graph was shown in Figure 7 
of this chapter. It is unnecessary to change any part 
of equation (49) except ATp/Tpo, since the use of Tp, 
in the rest of the formula (instead of Tpo) will result 
in only a small percentage change in the whole 
expression. For Tp/Tpo, however, it is now necessary 


5 2 Vl 4- 2/3 


J. ATp 
hi Tpo 

The coefficient hi is plotted in Figure 13. The factor 

^ ^ Tpe - Tpo ^ xke - v^o 
Tpo Tpo ^0 

is the relative error in release time due to the use of 
\po instead of ype- 

Figure 11 of Chapter 2 presents graphically the 
relation (49) connecting the variables *S, a, V when 
8 and K are assigned the values 100 feet and 
3, respectively. The figure was constructed as 
follows: 

If a fixed value is assigned to Tc/V, the right-hand 
member of equation (49) becomes a function of a 
only. Hence for each a a value of S can be com¬ 
puted. By assigning a values from 0 degrees up to 
60 degrees, and plotting <8 on a polar coordinate 
system, a curve is obtained along which a and S vary 
but Tc/V is constant. Eight such curves for Tc/V 


_ 

M \ Tpo 

p. -b cos a/ 

(49) 

to use 

Tpe - Tp, 

Tpi Vl 

Since Ve ~ Vi is much smaller than Ve — Vo, a great 
improvement is noted in the maximum range corre¬ 
sponding to a horizontal error of 100 feet at the 
target, especially for small dive angles and long 
ranges. 

6.4.5 from Incorrect Measure¬ 

ment of Dive Angle 

An error in the measurement of dive angle means 
that an incorrect value of V ''iH be used by the 
computer. This will cause an error in the release 
time. 

Let da and dTp be the errors in a and Tp. From 


1 + Vl + 2/3 
2/3 


V- - -( Vl + 2^ + J 

M + COS a \ 






























ERRORS AND INSTRUIVIENTAL ADJUSTMENTS 


109 



Figure 13 . b, = {ATp/Tp)/(8/S) versus Tc/V for 
different dive angles a; K = S; showing relationship 
between change or error ATp in Tp and resulting hori¬ 
zontal impact error 8 . 

equation (18) of Chapter 2, using logarithmic 
differentiation, we have 


Substitution from equation (51) into (49) gives 
the relation connecting 8/S with da in the abbre¬ 
viated form 8/S = (ba/b) da, whence 

5 = — da, (52) 

b sm a 

where sin a is the altitude at which pull-up 

began. 

It follows from equation (52) that 

_ 8 _ ba hi 

da b sin a 

With V = 250 V 2 knots (= 355 knots) and K = 3, 
the expression 

K , h 

b sin a 

is computed for several values of /12 and a = 10 
degrees, 20 degrees, ■ • • 60 degrees, and the corre¬ 
sponding values of — 8/da are shown graphically in 
Figure 14. 

Since ba/b is independent of hi and V except as 
they occur in the expression h 2 /V^ (or Tc/V), it 
follows from equation (52) that if V is multiplied 
by a factor V n and at the same time hy n, then 

— 8/da will be multiplied by n. For this reason the 
use of the factor n, with V in knots, in both the /12 and 

— 8/da scales of the graph makes the graph appli- 


dTpo 

Tpo 


tana + 


sin a 


2(K - 




+ 


8^/8a 




(50) 


but 


80 „r . . sina 1 

-— = /3 cot a -b - , 

5a [_ A — cos aj 


and equation (50) becomes 


dT. 


Tp„ 


where 


- ,1 . sin a 

ba = tan a -f ^ cot a 4-X 

2 


( 51 ) 


r . ■ - +._W—1 

La — cos a A — cos a VA(jA — cos a)J 

1 f . , sin a ^ 

— - , - I cot a + - } . 

2 V 1 -f- 2/3 ^ A — cos a' 


cable to any airspeed. For V = 250, 350, and 500 
knots, n = 3/^, 1, and 2, respectively. 

From Figure 14, reading values of corresponding 
to a given — 8/da at each dive angle, a spatial 
contour map (shown in Figure 15) of — 8/da, or 
— da/8, as a function of the release point, can be 
constructed. The airspeed factor n is again used in 
all scales which involve linear units. Additional 
points were obtained for the contour map by direct 
calculation for the case a = 0, when the relation 


giK - 1) ( - da/8) 

is valid. 

It will be noted that the contours resemble slant 
range arcs with centers at the origin, and therefore 
that da/8 is almost independent of dive angle at 
constant slant range. 




















no 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


^ ^ ^ Range Error Due to Error in Tp 

A certain range error must be expected because 
accumulated errors in the component parts of the 
bomb director result in an error in the release time. 
If a particular order of accuracy, such as one per 


DEGREES PER HUNDRED FEET 



-(f/doCiN FEET PER DEGREE 


Figure 14. Relationship between error da in dive angle 
and resulting horizontal impact error 5. Ratios — b/da 
and —da /8 versus altitude 82 = S sin a for different 
values of a; K = S. Scale factor n is determined by 
velocity: n = 3^ when T' = 250 knots, n = 1 when 
1' = 350 knots; n = 2 when T = 500 knots. 

cent in Tp, is demanded of the mechanism, it is 
possible to calculate from equation (49) the hori¬ 
zontal error 5, 

Figure 16 shotvs graphically the results of such 
calculations. The curves in Figure 16 are strictly 
valid for the zero order solution and, except for 
second order terms, valid for the first order and exact 
solutions. The curves give the ranges corresponding 
to given percentage errors in the calculation of 
release time ATp/Tp, which will result in a ground 
error of 100 feet. At close ranges computer errors 
naturally can be permitted to be larger without 
affecting the ground accuracy adversely. A com¬ 
puter having one per cent accuracy permits slant 
ranges of the order of 15,000 feet. 


The next consideration is whether toss bombing 
results are limited more by approximations involved 
in the early solutions of the equations, or by lack of 
instrumental accuracy. From Figure 16, it can be 
seen that an error of two percent in Tp results in about 
the same error as is inherent in the 4'o solution at 
350 knots, slant ranges being the same. In general, 
since the error is negative, it can be reduced some¬ 
what by depressing the sight slightly. 

The relative importance of these two types of 
error depends strongly upon velocity, as Figure 16 
shows. Figure 16 represents a superposition of the 
100-foot error curves fon/'o on the computer accuracy 

BIVE angle 



Curve A B C D E FG H KL 

—da /8 in degree.s per 100 ft 123456789 10 


n n n n n n n n n n 

Figure 15. Pictorial chart of pull-up points corre¬ 
sponding to different ratios of dive angle error da to 
resulting horizontal imjiact error 8 ; K = 3. Scale 
factor n determined by velocity as in Figure 14. 

curves. For small velocities the effect of \p function 
variations will outweigh instrumental errors. How¬ 
ever, if it is desired to take advantage of the long 
ranges theoretically possible at high velocities, the 
accuracy of the computer must be increased con¬ 
siderably. 

^ Range Errors 

Due to Altimeter Errors 

In this section the effects produced by errors in 
altimeter indications on the time-to-target Tc are 
examined. 


















ERRORS AND INSTRUMENTAL ADJUSTMENTS 


111 


Let hi and /12 be the true altitudes at which the 
altimeter operates. Also let hio and h 2 o be the 
nominally correct altitudes;then/tio//i 2 o = 6/5. Define 
Cl and €2 by the relations 

hi = hio{l + Cl) hi = /!2o(1 + € 2 ); (53) 

Cl and C 2 are the relativ^e errors in the altitudes. 
Define by the relation 

^ = ^“(1+ €,) = 5(1+ O; (54) 

hi hio 5 

€r is the relative error in the mea.surement of hi/hi. 

If Tii is the actual time it takes the aircraft to fly 
betw'een the two altitude points, then 

_ ^1 - hi 

J 12 - —-r-• 

V sm a 

By using equation (54) to eliminate hi, we obtain: 

Tu = (1 + 6«.) . (55) 

oV sm a 


Since 

rp _ hi 

— y—; , 

V sm a 

it follows that 

Ti2 = “ (1 + Ge,.), 

5 

and 

ATc = Tc- 5Tii = - QTc c,. (56) 

The presence of the negative sign shows that 
when Cr is negative, i.e., hi/hi < 6/5, then ATc w'ill 
be positive, so that the measured time-to-target 
57\i W'ill be too small and the bomb will go short 
of the target. Moreover, any error is reflected in a 
relative error six times as large in Tc. 

Range errors due to errors in c^ are shown in 
Figure 17 for div'e angles of 30 degrees and a plane 
speed of 250 knots. These range errors decrease for 
increasing dive angle and plane speed. In Figure 18 


45* 


DIVE ANGLE 
60* 


75* 


90* 



Figure 16. Pictorial chart of pull-up points for which 1, 2, and 4 per cent errors in Tp are required to produce 100-foot 
horizontal impact error, at different velocities; ^ = 3. 






































112 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 



Figure 17. Graph of horizontal impact errors d result¬ 
ing from different relative errors in altitude ratio 
ht/hz, as function of hz] V = 250 knots, a = 30 degrees, 
/C = 4. 


PULL-UP altitude- h2-1000 FEET UNITS 



Figure 18. Graph of altitude ratio error e,. required to 
produce 50-foot horizontal impact error, as function of 
hz, for different dive angles and for velocities between 
250 and 500 knots; K = 4. 



HORIZONTAL RANGE ERROR-FEET 

Figure 19. Altitude ratio error versus horizontal range error, resulting in horizontal impact error 5, for different 
dive angles a; V = 500 knots, hz = 5,000 feet, K = 4. 




























































































































































ERRORS AND INSTRUMENTAL ADJUSTMENTS 


113 


are plotted contours corresponding to the altimeter 
ratio errors which will produce a horizontal range 
error of 50 feet at the various dive angles indicated. 
The shaded area is bounded by two curves, one for a 
plane velocity of 250 knots (the lower curve) and 
the other for a plane velocity of 500 knots (the upper 
curve). 

Figure 19 shows how the altimeter ratio error 
affects the horizontal range error as the dive angle 
is increased from 10 degrees to 60 degrees. 

From equations (53) and (54) it follows that 


€l — €2 

1+62 


= Cl — €2. 


Hence, if 6 i = 62 , then must be zero. That is, 
equal relative errors in hi and /i 2 cause to be zero, 
and therefore ATc = 0 by equation (56). However, 
if 61 = — 62 , then 6 ^ = 2 61 , so that ATc = — 12Tc6i. 
This shows the importance of having errors which 


come into hi and h 2 in the same sense, both positive 
or both negative. 

It is also possible to express 6 ^ in terms of target 
altitude error or, what amounts to the same thing, 
equal errors in hi and h 2 . Thus, let hi = hio + Ci 
and /?2 = h 2 o + 62 - Then, by equation (54) 


5ei — 6e2 



This shows that if Ci = 62 , then 6 , Avill be quite 
small, but if 

Cl ^ - 62 , 

then 


Cr 




llCl 

6/22 


This brings out again the importance of preventing 
errors of opposite sign from occurring in hi and h 2 . 

Table 10 shows the maximum permissible errors 
in altitude that will produce a ground error of 50 feet 


Table 10. Maximum permissible error in altitude that will produce error on ground of 50 feet or less. 
(Case where errors have like signs at first and second altitudes.) 


Altimeter 

prong 

No. 

Second 

altitude 

(ft) 

Plane 

velocity 

(knots) 

10 

20 

Errors in altitude (ft) 
Dive angle (degrees) 

30 40 

50 

60 

11 

1,389 

250 

< 21 

40 

90 

224 

431* 

431* 



500 

< 21 

100 

345 

431* 

431* 

431* 

10 

1,667 

250 

< 25 

39 

85 

210 

518* 

518* 



500 

< 25 

92 

299 

518* 

518* 

518* 

9 

2,000 

250 

< 30 

37 

81 

175 

359 

621* 



500 

< 30 

66 

224 

621* 

621* 

621* 

8 

2,400 

250 

<35 

37 

75 

136 

292 

523 



500 

< 35 

60 

173 

455 

745* 

745* 

7 

2,880 

250 

<43 

43 

71 

135 

259 

444 



500 

<43 

49 

150 

366 

763 

894* 

6 

3,456 

250 

< 52 

< 52 

67 

122 

223 

391 



500 

< 52 

< 52 

137 

295 

614 

1,072* 

5 

4,157 

250 

<74 

< 74 

<74 

109 

204 

355 



500 

< 74 

<74 

123 

255 

511 

1,181* 

4 

4,977 

250 

<74 

<74 

<74 

97 

192 

314 



500 

<74 

< 74 

111 

223 

417 

947 

3 

5,977 

250 

< 88 

< 88 

<88 

99 

181 

306 



500 

< 88 

< 88 

92 

192 

402 

767 

2 

7,200 

250 

< 106 

< 106 

< 106 

< 106 

173 

293 



500 

< 106 

< 106 

< 106 

201 

360 

602 


* This error in altitude will produce an error on the ground of less than 50 ft. 

< Error in altitude should be less than given value in order to produce an error on the ground of 50 ft. 

The range of values for which the curves in this report were plotted give rise to the above limitations in the use of Table 10. 













114 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


Table 11 . Maximum permissible error in altitude that will produce error on ground of 50 feet or less. 
(Case where errors have opposite signs at first and second altitudes.) 


Altimeter 

prong 

No. 

Second 

altitude 

(ft) 

Plane 

velocity 

(knots) 

10 

20 

Error in altitude (ft) 
Dive angle (degrees) 

30 40 

50 

60 

11 

1,389 

250 

<2 

4 

9 

24 

55* 

55* 



500 

<2 

10 

40 

55* 

55* 

55* 

10 

1,667 

250 

<2 

4 

8 

22 

66* 

66* 



500 

<2 

9 

33 

66* 

66* 

66* 

9 

2,000 

250 

<3 

3 

7 

17 

39 

79* 



500 

<3 

6 

23 

79* 

79* 

79* 

8 

2,400 

250 

<3 

3 

7 

13 

30 

59 



500 

<3 

6 

17 

50 

94* 

94* 

7 

2,880 

250 

<4 

4 

7 

13 

26 

47 



500 

< 4 

5 

14 

38 

91 

113* 

6 

3,456 

250 

<5 

< 5 

<6 

11 

22 

39 



500 

<5 

<5 

13 

29 

66 

136* 

5 

4,157 

250 

<6 

<6 

<6 

10 

19 

35 



500 

<6 

<6 

12 

25 

52 

145 

4 

4,977 

250 

<6 

<6 

< 6 

7 

9 

18 



500 

<6 

<6 

10 

21 

41 

104 

3 

5,977 

250 

<8 

<8 

8 

9 

17 

29 



500 

<8 

<8 

9 

18 

39 

79 

2 

7,200 

250 

< 10 

< 10 

< 10 

< 10 

16 

28 



500 

< 10 

< 10 

< 10 

19 

34 

59 


* This error in altitude will produce an error on the ground of less than 50 ft. 

< Error in altitude should be less than given value in order to produce an error on the ground of 50 ft. 

The range of values for which the curves in this report were plotted give rise to the above limitations in the use of Table 11. 


or less if the errors have the same sign, while Table 11 
gives corresponding figures if the errors have different 
signs. 

The errors which may occur when using an 
altimeter with bomb tossing equipment may in 
general be classified as either instrumental errors 
or as errors inherent in the barometric method for 
measuring altitude. Among these errors are the 
following: 

1. Scale errors. 

2. Friction errors. 

3. Position errors. 

4. Lag in the static line. 

5. Lag in the altimeter capsule. 

6. Deviation of the temperature of the air column 
from that assumed in the standard atmosphere. 

7. Atmospheric pressure at the target level. 


8. Errors in the setting of the prongs. 

9. Vibration. 

In general, lag and scale errors have like signs at 
the first and second altitude points. Also, a shift in 
atmospheric pressure at the target level, from the 
assumed value, is of the nature of a lag (positive or 
negative). The other errors listed may cause errors 
of either sign at both altitude points. 

Reference to Table 10 shows that for all prongs, 
all airspeeds, and for dive angles greater than 20 de¬ 
grees, a net error in altitude at any one altitude 
point of 40 feet or less is permissible for a horizontal 
ground error of 50 feet or less provided the errors in 
adjacent altitude points are of like signs. 

Table 11 serves to highlight the importance of 
eliminating random effects such as might be due to 
vibration. The bomb tossing altimeter was mounted 
on a suitable shock mount for this as well as for 
other reasons (see Section 3.5.4). 









ERRORS AND INSTRUMENTAL ADJUSTMENTS 


115 



Figure 20. Nomographic chart for determining change ATp in Tp corresponding to given shift 5 in impact point (and vice versa). 

























































































































3S0 n 


116 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


1 


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Figurk 21. Nomographic chart for determining intervalometer setting required for given ground spacing of bombs. 











































































































ERRORS AND INSTRUMENTAL ADJUSTMENTS 


117 


* Stick Offset^ 

The stick offset provides a means of systematically 
decreasing the release time to drop bombs short of 
the target. It is used when sticks or trains of bombs 
are released or when torpedoes are tossed (see Sec¬ 
tion 6.4.10). When sticks of bombs are released the 
stick offset provides for bracketing of the target by 
having the first bombs released to fall short of the 
target and the last one beyond. Controlling factors 
in selecting the setting are (1) the amount short of 
the target by which the first bomb should strike, and 
(2) the intervalometer setting which determines the 
time interval (or ground spacing) between the bombs 
in the train. 

Computations for determining the settings are 
based on equation (35) in Avhich horizontal error 8 
(or displacement in this case) is related to shift in 
release time ATc. The details of the computations 
are given in reference 40. The summary of the 
calculations can be reduced to nomographic charts, 
as shown in Figures 20 and 21. 

Short Impact Charts 

Figure 20 allows the estimation of a short release 
time ATc, to give an impact short of the target for 
the first bomb in the train. To use the chart proceed 
as follows: 

1. Locate the point on line A1 corresponding to 
the altitude at the start of pull-up, and the point on 
line A2 corresponding to the plane’s airspeed. 

2. Join these two points with a straight line and 
extend this line until it intersects line A3. 

3. From this point of intersection with A3 draw 
a vertical line up to the curve marked with the 
correct dive angle. (For intermediate dive angles, 
interpolate between two curves.) 

4. Through the point so determined on the curve, 
draw a horizontal line to the left to intersect line A4. 

5. Join this point on line A4 with the point on 
line A3 corresponding to the airspeed (same value 
as on line A2) and extend this straight line to inter- 
.sect line A6. 

6. Join this point on A6 with the point on line A7 
corresponding to the desired amount by which the 
first bomb of the stick is to fall short of the target. 

7. Extend to line A8 the line determined in G 
above. Where it intersects A8, read the value of the 
stick-length offset ATc. 


Intervalometer Chart 

Figure 21 allows the selection of a stick spacing 
(FAT) to give proper bracketing of the bombs on 
the target. To use the chart proceed as follows: 

1. Using the intervalometer setting chart, pro¬ 
ceed first as in paragraphs 1, 2, 3, under (1) above, 
using lines Bl, B2, and B3. (Note that this second 
chart has a different set of curves.) 

2. Through the point so determined on the curve, 
draw a horizontal line to the left to intersect line B4. 

3. Join this point on B4 with the point on line Bo 
corresponding to the pull-up acceleration (K) of the 
plane at release. AMiere K varies, the value at 
release of the central bomb of the stick should be 
used. Extend this straight line to intersect line BG. 

4. Join this point on BG with the point on line B7 
corresponding to the desired ground spacing 8 
between successive bombs. (The spacing between 
bombs will not be exactly uniform, but will center 
about the value used on line B7.) 

5. Extend to line B8 the line so determined. At 
the intersection read the value of the intervalometer 
setting (FAT). The intervalometer dial marked 
“spacing between bombs” should be set for this 
value, in order to obtain an actual spacing 5 (as in 
4 above). 

The sample calculation (broken lines w'ith arrows) 
on the two charts illustrates the method described 
above. A plane dives at an angle of 40 degrees wdth a 
true airspeed of 290 knots in the direction of the 
target, and starts to pull up when its altitude is 
2,G00 feet. A stick of 5 bombs is to be released, and 
it is desired to space these bombs 90 feet apart and 
to have the third bomb hit the target; hence the 
desired distance short (D) for the first bomb is 
180 feet, and the desired ground spacing (S) 90 feet. 
Moreover, it is estimated that the pull-up accelera¬ 
tion during the period of release of the 5 bombs will 
average 3.1^. The calculations on the two charts 
show that the stick-length offset (ATc) for this case 
must be 2.05 seconds, and the intervalometer setting 
(FAT) 58 feet. 

The charts may also be used in converse manner to 
determine one of the other quantities (e.g., 8, h, K, a) 
wEen ATc or Fat is known. 

In addition. Figure 21 may be used for determining 
the error on the ground resulting from a known error 
in release time, ATp. In this case, FATp is entered in 
scale J and the ground error is read from scale I. 

It should be pointed out that the construction of 








118 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


the charts is based on the assumption that it is 
possible to provide an instrumental adjustment, 
ATc, on the stick offset dial which will not vary as a, 
Tc/V, etc., vary. In actuality this is only approx¬ 
imately true, since the design of the biasing circuit 
used in the stick offset adjustment is such as to 
provide some variation of ATc with a and Tc. The 
variation of the actual short offset in seconds as a 
function of ATc, the stick offset setting, has been 
given in equation (34). In this connection the 
stick-offset nomograph given in reference 144 should 
be consulted. The reference chart uses the dial set¬ 
ting ATc instead of the theoretical offset ATc. 

MPI Adjustment 

The MPI adjustment dial introduces a percentage 
change in release time which is independent of Tc 
and a. The effect of the MPI adjustment is shown in 
Figure 13 of Chapter 2 for the Mark 1 Model 1 bomb 
director. This figure was obtained from the chart in 
Figure 20 in the following way. 

For a given airspeed, dive angle, and altitude, it 
w'as possible to calculate Tc. Since each division on 
the MPI dial corresponds to a fixed percentage 
change in Tc (3.4 per cent per division was used) 
ATc could be computed. From Figure 20 the corre¬ 
sponding impact distance D w'as determined. 

6.4.10 Torpedo Tossing Theory 

Application of the bomb director to torpedo toss¬ 
ing is another example of the functional relation¬ 
ship betw'een the impact point on the ground and the 
stick-offset or ATc adjustment. 

In order to toss torpedoes it is required to de¬ 
termine the ATc which will give an optimum opera¬ 
tional range of dive angle and altitude. This design 
value of ATc was taken as the value w'hich w^ould 
place the torpedo exactly 450 feet short for a ma¬ 
neuver initiated at a dive angle of 25 degrees and a 
second altitude of 1,395 feet. The intervalometer 
chart does not provide sufficient accuracy to be 
useful in this connection, since the ATc required is 
of the order of 50 per cent of Tc, so that curvature 
effects are no longer negligible. 

Approximate Solution for Design Purposes 

The followdng procedure was used to determine an 
accurate value of ATc for this purpose. 


The problem is to find the release time, Tp (refer¬ 
ences are to Figure 10, Chapter 2) required to make 
the torpedo hit the point K' which is located at a 
distance 8 = — 450 feet from the target at point H. 
The coordinates of the impact point K' are 

rr . .. COS a\ 

Xk’ = -S 4- 5 cos a = F \Tc + — j 

(57) 

= 4- 5 sin a 

where S is the slant range. 

The y-coordinate of the torpedo at anytime t > Tp, 
is given by the second equations (8), Chapter 2, 
w'hich at time t = Th', y = 4- 5 sin a becomes 
cos a {Th> — TpY — iigTp {Tw — Tp) 

— \^lgTY-\- 5 sin a = 0. (58) 

For 5 = 0, equation (58) leads to the usual solution 
given in Chapter 2. Similarly, the solution of equa¬ 
tion (58) is taken as 

■ Tk- -Tp = cTK'Tp (59) 


w'here 


(Xr' 


(jR' 





4- cos a 



25 sin a\ T 

gTY /J 


cos a 


m4-m^ 



5 sin 2a Y 

ngTY ) 


cos a 


(60) 


Similarly the a:-coordinate of the bomb at any time 
f > Tp is 

X = Vt 4- Ig sin a (t — Tp)"^, (61) 


w^here higher order terms in Tp arising from the 
expansion of the cosine of the pull-up angle have 
been neglected. Forf = Tr>, x = Xr'. Using equa¬ 
tions (59) and (60), (61) has the solution 


T, 


lifTR' + 1 ) 

2 cr ;,,2 



4(rj^'“ 

IUk' + 1)^ 



5 



(62) 


Equation (62) will give the value of Tp w'hich will 
cause the bomb to hit point K' provided the correct 
value of (tr' is used. The latter, in turn, is a function 
of Tp so that a method of successive approximations 
may be employed in evaluating Tp. That is, assume 
a value for Tp. Next, calculate (tr' using equation 
(60). Using this value of cr', compute T^, from equa- 











ERRORS AND INSTRUMENTAL ADJUSTMENTS 


119 


tion (G2). This new value of Tp may then be inserted 
in (60), etc. The closer the originally assumed value 
of Tpis to the correct value, the more rapidly will 
the successive approximations of Tp converge to the 
correct value. The first approximate value may be 
that for which the trajectory crosses the collision 
course at an altitude equal to 5 tan a. Another 
po.ssibility is to use the approximate value indicated 
from the intervalometer chart. The approximation 
method converges in either direction; i.e., the orig¬ 
inally assumed Tp may be either larger or smaller 
than the correct value. 

This approximation method was carried out for 
the case where 5 = —450 feet, a: = 25 degrees, 
V = 250 knots, K = 3, and a .second altimeter 
contact at 1,395 feet. In order to allow for the time 
which elapses between the signal to start the pull-up 
and the initiation of the pull-up, the nominal alti¬ 
tude of 1,395 feet was changed to 1,210 feet wdiich 
corresponds to an allow'ance of approximately one 
second for pilot and aircraft reaction time. For the 
above values, Tp turns out to be 

Tp = 0.472 second (5 = -450 feet). 

From this value of Tp, the ATc required may be 
determined fi'om the equation 

T _ \T 

Tp = ^ -Ao (63) 

K + VA'2 - K 


The results given by the equation (65) are com¬ 
pared with those obtained from the trajectories in 
the follow'ing table for FA7’c = 1,570 feet: 


PuII-up \S in feet 

Dive angle altitude (ft) Computed From Figure 31 


25° 

1,210 

30 

1,600 

1,650 


2,880 

320 

1.890 

1,935 


4,150 

830 

2,400 

2,550 

15° 

1,362 

210 

1,780 

1,780 


2,000 

570 

2,140 

2,160 


It will be seen that equation (65) gives values for 
A8 w'hich are in reasonable agreement with the 
observed values. 

Exact Solution for Tp (with Target off 
Collision Course) 

On making the substitutions 

_ V- sin dp _ F-(l — cos dp) 

Xp - Dp — - 

giJ- 

Xp = V cos dp ijp = V sin dp 

in equations (8) of Chapter 2, and taking account of 
equation (57) w^e have: 

VTc — \gTf-^\\\a + 5 cos a 


where 


Tp = 0.472 second 
Tc = 6.781 seconds 
K = 3 

\po = 0.84 (K = 3, a = 25 degrees, Tc/V = 0.016). 
Solving for ATc, the result is 

ATc = 3.719 seconds. 


The operational limits resulting from the use of this 
value’of ATc are given in Figure 19 of Chapter 2. 

One feature of the trajectories of this figure wdiich 
requires further discussion is the fact that they do 
not all cross the collision course at the same point. 
That is, since S = VTc h is to be expected that 
AS = VATc. This w'ould be true were it not for the 
fact that the Model 0 integrator computes a release 
time wdiich is slightly in error. As a consequence 
there is an error in slant range in the amount of: 


Y ( 1 - /vVm' ) rp 3 

. - I pQ . 

21 cos 


(64) 


The actual intersection point with the collision 
course is then given by: 

A*S = VATc + es. (65) 


+ VT/cos dp 
gt^ 


( 66 ) 


Y1 

gn 


— \gTp cos a — b sin a 


- YT; sin«p 

gp- 


wdiere T/ = Tk' — Tp is the time from release to the 
point K'. 

Squaring both members of each equation (66) and 
adding member by member, it is found that dp is 
eliminated, leaving 


1 

4y 


- T/^ -fl 4- - cosa + gTc^\rj.,. ^ 
\ ji V / 


, 5-' , 2bTc 2b . „ 

4-h - cos a — — sm a = 0. (6C 

V^ V gp 

As in the case of equation (7), the-solution of equa¬ 
tion (67) desired here is 


T/ = J (Vfi - Vr2), 


( 68 ) 


















120 


MATIIEMATICAL ANALYSIS OF BOMB TOSSING 


where 


r. = 1 + + 0l‘ (D + sin .). 

M 1 

. , COS a gTc ... .V 

12 = 1 + —3- - ^- sin a), 
^x T" 


and 


D 




1 + 


v^t:- 


+ 


25 cos a 

vr. 


25 sin a 
gp-Tc~ 


It is now necessary to solve eciuations (66) for dp. 
Following the same procedure as before, let the first 
be multiplied by 1 — cos dp, the second b}" sin dp, and 
the equations then be added member by member. 
The resulting relation is linear in the quantity 

, dp sin dp 

w = cot — = - - —, 

2 1 — cos dp 

and its solution is 

^ TTc + 5 cos a + VT/ - Iff 77^ sin o; 

5 sin a + cos a 

It remains to replace 7’/ in equation (69) by its 
value from equation (68) and express the result in as 
simple a form as possible. After some algebraic 
reduction the formula (70) for co' is obtained. 

1 


5 sin 2a: + (5 + FTc cos a)- 


X 


u.se with machine guns. This standard sight align¬ 
ment corresponds to a sight line which is approx¬ 
imately 25 to 35 mils below the flight line under 
average loading conditions of a number of fighter 
bomber aircraft at a dive angle of 40 degrees and 
average indicated airspeeds of 300 to 350 knots. 

In Chapter 4, and particularly in Section 4.2.3, a 
standard flight test procedure is described for adjust¬ 
ing the sight line to coincidence with the flight line. 
In certain cases it may happen that complete 
adjustment is not possible, or that a residual mis¬ 
alignment error occurs. Such errors may be corrected 
instrument ally'' by making use of the MPI adjust¬ 
ment. Such an instrumental correction is ordinarily’’ 
made only^ once, for the particular set of flight condi¬ 
tions existing during the sight alignment test. At 
other values of airspeed, dive angle, and range, it is 
not necessarily' true that the instrumental adjust¬ 
ment will compensate for the sight misalignment. 
In addition, when dive angle, airspeed, and weight 
vary', the angle of attack of the aircraft changes, 
resulting in a change in the angle between the sight 
line and the flight line. The errors resulting from 
such misalignments and means for correcting them 
will be discussed here. 

Figure 22 repre.sents the flight of plane and bomb 
for the case in which the line of flight makes a con- 


VTc cos a; 


1 D (VPi + VPs) + VPiF 




cos 2a + _1- sin a (V Pi — V Pg) + V I 


(70) 


On setting 5 = 0, equation (70) reduces, as it should, 
to equation (12) of Chapter 2. 

The pull-up angle is now given by' 

dKe = 2 arc tan ^ (71) 

0 }' 

and the period from the beginning of pull-up until 
the release of the torpedo is given by' 

Tp/ = ^ arc tan ^. (72) 

giJL io 

6.4.11 Sigjit Alisalignment and Angle 
of Attack Variations 

One of the fundamental requirements for utilizing 
the tossing technique is that the sight line and the 
flight line coincide. The standard sights used in most 
aircraft are aligned with the boresight datum line for 


stant angle 4> with the sight line, the sight being kept 
on the target Tv'until pull-up. The vectors marked S 
represent instantaneous directions of the sight line, 
alway's directed toward the target; those marked F, 
making an angle (f) with the S vectors, represent the 
corresponding instantaneous directions of flight. 
It will be noted that the path AO is slightly' concave 
upward; it would be concave downward if 0 had 
the opposite sense. For small angles, however, very 
little sacrifice of accuracy results from assuming 
that the arc AO is straight. 

If A is the first altitude point, the values of dive 
angle, time to target, and airspeed which are fed into 
the computer are determined by conditions along AO, 
assuming that the dive angle gy'ro is aligned with 
respect to the flight line. Barring other errors, there¬ 
fore, the release time ^^ill be so determined as to 
cause the bomb to pass through point H on the 

















ERRORS AND INSTRUMENTAL ADJUSTMENTS 


121 


extension of AO. The horizontal error due to the 
misalignment of the sight is then 5 = K'H. 

As regards conventions of sign, the angle (j) is 
considered positive when the sight line is above the 
flight line, and the error 8 positive w'hen the impact 
is beyond the target. In Figure 22, 4> is positive and 
8 is negative. 



Figure 22. Flight and trajectory diagram with mis¬ 
aligned sight. Vectors marked S and F represent instan¬ 
taneous directions of sight line and flight line, respec¬ 
tively. 

The relation between 0 and 8 is obtained by apply¬ 
ing the law of sines to the triangle OHK'. If 
Oil = S = VTc, then 


sin (j> sin fa — </>) sin afcot cj) — cot a) 

(73) 

If 1 0 1 is small compared wdth a, an approximation to 
(73) is 

8 = or S = — - sin a, (74) 

sin a 4) 

4> being measured in radians. The relative error in 8, 
as given by ecpiation (74), is slightly less than 5 per 
cent if I (/) I < 1 degree and a > 20 degrees, and less 
than 10 per cent if 1 I < 1 degree, and a > 10 
tlegrees. 


If a and as related in equation (74) are plotted in 
polar coordinates, a circle is obtained for each value 
of 8i4>, as shown in Figure 23. These circles have their 
centers on the line a = 90 degrees, and the diameter 
of each is the corresponding value of | 5/0 | as labeled 
in the figure. 

From the exact equation (73) it is seen that 5 is 
proportional not to 0 but to 1/(cot 0 — cot a), w^hich 
differs significantly from 0 when a is small or 0 is 
large. The graphs of Figure 23, therefore, become 
accurate for all a and 0 if the feet per mil values wdth 
which each circle is labeled are considered as values 
of — l,0005(cot 0 — cot a) instead of values of —5/0. 

The error due to noncoincidence of sight and flight 
lines would be eliminated, causing a hit on the target 
K', if the value of Tc fed into the computer w'ere 
adjusted to correspond to a target at H' instead of H. 
This would mean a relative increase ec = ATc/Tc (or 
a relative decrease — ATc/Tl, where VATc = HH' 
and ATc/T, = HH'/OH. 

Formulas for ec wall now- be obtained. An applica¬ 
tion of the law of sines to triangle HH'K' in Figure 
22 yields the relation 

VAT, ^ 
sin (a 4- 0/) sin df,' 

It follows that 


ATc _ FA^c _ - 5 sinfg -f g/) ^ _ 56 sing 
Tc S S sin 0/ S 


(75) 

where 

sin (g + Oh) . . , . , 

0 = -^-^ = cotg + cot0/. (/6) 

sin g sin 0/ 

Taking the value of cot 0/ from (39) permits (76) 
to be brought to the form 

1 , tan g + cos dp 


0 = 


_ - + - 

sm g cos g / 

V'+VT 


2 cost 


(77) 


/l(l + cos dp') 


An approximate formula for 0 is obtained by 
replacing 1 + cos dp' by 2, cot dp by \/dp', and making 
use of the formula for dp' immediately preceding (45); 
this formula is 


0 = 


+ 


tan g 


in g cos g / l 

V1 + — cos g 


X 


2^ 


1 + ^ cos g j 


. (78) 






























122 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


When 1 I is small compared with a, equations 
(74) and (76) yield the approximate relation 

Cc ^ Q4>. (79) 

The remarks concerning the degree of accuracy of 
(74) as a formula for 6 apply equally to (79) as a 
formula for Cc. 

With the notation expressed in equation (80), 


equation (78) in a form solved for /3 is equivalent to 
/3 = 4/(1 + W)- 

Since 


.8 = T'7’ = 


+ cos a) 
gjl sin a 


M = 


tan a 




X 


1 + 


1 




1 : 1 

1 + - COS a 
U 


1 


1 + — cos a 
M 


0 - 


tan a 


sin a cos a ^ 


^ I 1 

1 + - cos a 
M 


(80) 


DIVE ANGLE 


45" 60" ' 75" 90" 



Figure 23. Effect of misaligned sight on impact point. Pictorial chart of pull-up points corresponding to different 
ratios of horizontal impact shift 5^ to angle of misalignment (f) producing shift (independent of F and K). Each curve 
corresponds to constant value of given \n feet/mil by numerals on respective curves (5 to 55 feet/mil). 























ERRORS AND INSTRUMENTAL ADJUSTMENTS 


123 


it follows that 

g _ F-(/z + cos a) 


M(l + p/). 


( 81 ) 


gU sin ot 

Figure 24 is a contour map constructed from 
equation (81) using 0 = tc (/> in calculating the 
value of M in equation (80). Figure 24 shows the 
various slant ranges and dive angles which corre¬ 
spond to a given value of 0. 

As in the case of Figure 23, Figure 24 becomes 

DIVE ANGLE 

45® 60 


is in mils. The curve marked 0.8 per cent per mil, 
for example, is also the locus of 0 = 8. 

Figure 25 is a contour map constructed from 
equation (75) for the ratio 5/ ec, i.e., the linear 
impact error for each per cent change in In 
Figure 25 both changes have the same sign. Further¬ 
more, the reciprocals of the | 5/ ed figures on the 
curves represent the per cent change in Tc required 
to offset each foot of impact error; and when so 


75* 


90* 



Figure 24. Relation between angle (f) of sight misalignment and relative change e = ATc/Tc required to offset its 
effect. Pictorial chart of pull-up points corresponding to different ratios ej(}); K = S. Scale factor n determined by- 
velocity: n = 14 when V = 350 knots; n = 2 when V = 500 knots. Value of ec/</> represented by each curve is given in 
per cent/mil by numeral on curve (0.5 to 1.2 per cent/mil). 


inaccurate for very small a or very large (j), but 
becomes accurate for all a and (/> if the figure 
attached to each curve is considered as the value of 
l,000ec(cot (/) — cot a) instead of the value of ec/4>. 

Figure 24 can be interpreted as a contour map 
of the function 0. When so considered the “per cent 
per mil” figures must be converted by multiplication 
by 0.01 /O.OOl = 10, since is a percentage and 0 


interpreted, 5 and tc have opposite signs. Thus this 
figure is of a general nature, applicable not only to 
the sight error problem but to all problems involving 
correction of an impact error by adjustment of Tc. 
The curves of Figure 25 w'ere plotted by noting that 

5/0 

and making use of Figures 23 and 24. 



















124 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


Application of the preceding discussion and of 
Figures 23 and 24 requires that the value of the sight 
error (f) for any specific case, or at least the difference 
between (f) values for two specific cases, be known. 
The effective sight error, however, depends not only 
on the fixed orientation of the sight with respect to 
the airplane, but also on the angle of attack, or 
orientation of the plane with respect to its flight line. 
The variation of the latter with airspeed and dive 
angle is appreciable and must be taken into account. 


depends on the choice of a reference line in the air¬ 
plane, and for purposes of calculating differences in 
angles of attack one may set k = 0 with no loss of 
generality: 

(83) 

It is found generally that C has the same value for all 
planes of a series, as TBM-l and TBM-IC. 

The nomogram of Figure 26 gives this relative 


45* 


DIVE ANGLE 
60* 


75« 


90“ 



Figure 25. Relationship between relative change ec in Tc and resulting horizontal impact error 5c. Pictorial chart of 
pull-up points corresponding to different ratios 5c/tc represented by each curve is given in feet/per cent by numeral on 
curve {on to 60n feet/per cent). 


The angle of attack (f)a is given by the formula 
. CTFcosa 

( 82 ) 

where W is the gross weight of the plane, and C and k 
are constants for any one plane. The value of k also 


angle of attack (/)a, as in equation (83), as a function 
of C, TF, V, and a. The calibrations on lines G, H, K, 
and M, have been determined from values of log C, 
log W, log V, and log cos a, respectively. Points on 
line J have been predetermined for each plane at its 
nominal weight, thus obviating the use of lines G and 


















ERRORS AND INSTRUMENTAL ADJUSTMENTS 


125 


O 

I 


< 

H 

(/) 


O 

L O 

TBM • 
(TBF)-^ 

\ 


P-38L 


SB 2C- 


F6F 
P-38L y 


\ 

--24 
--I50 ::23 

.. \ :-22 / 

\ --2I / |P-5IK 

: \:^ / 

/ 

>1-16 / 

} / ' 

■^/ -%/ ,’|-F4U 

Uoo^ J.IjV 


F4U 

(FG) 


FM 


P-5IK-I-350 


to 

CD 

_j 

o 

o 

o 


h- 

to 

to 

o 

cr 

o 


\ 


-■ Si 
: / \\Z 




10 


\ 


/; 


\ 


<250 / 

(F4F)-[ ^^-1-8 4-TBM 


/ 


/ 


\ 

47 ^ 


\ 


/ 


■ / -16 
--300 

: / 

• / 

■7 

7 




F6F 


FM 


Q ^ 



■50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

-34 
--33^ 

+ 32- 
-1-31 q: 
P £ 

to 

z 

o 

to 


+ 12 


:l|l 


--I0 


-■9 


X 

UJ 


--8 


0 


Figure; 26. Nomogram for determining changes in angle of attack (0a)- For planes at approximately nominal weight 
(e.g., P’4U, 12,000 pounds), start with designated points on line J, already predetermined by dashed lines through lines 
GandH. Examples: for F6F plane at nominal weight, (l)if F = 350 knots (line /I), decreasing a from 40 degrees (line C) 
to 30 degrees (line B) increases angle of attack by 16.9 — 14.9 = 2.0 mils; (2) if a = 40 degrees (line E), decreasing F 
from 350 (line F) to 300 knots (line D) increases angle of attack by 20.4 — 14.9 = 5.5 mils. 


















126 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


H whenever the gross weight is approximately 
nominal. 

Lines G through N have been so spaced that air¬ 
speed, V, and dive angle, a, may be entered in either 
order. This property is illustrated by the example 
appearing on the nomogram. The intersection of 
line A and line L, corresponding to an F6F at 350 
knots, may be joined with several points in turn on 
line M to obtain 0a on line N for different dive 
angles at the fixed airspeed; this is illustrated by 
dashed lines B and C for dive angles of 30 and 40 
degrees, respectively. On the other hand, the inter¬ 
section of line E and line L, corresponding to an 
F6F at 40 degrees dive angle, may be joined with 
points on line K to obtain 0a for different airspeeds 
at the fixed dive angle; this is illustrated by lines 
D and F for airspeeds of 300 and 350 knots, respec¬ 
tively. The relative convenience of the two methods 
depends on whether one is concerned more with 
variation of 0o with dive angle or with airspeed. 

According to equation (83), the angle of attack, 
while independent of range, is increased by a decrease 
in either airspeed or dive angle. Hence the range of 
variation in 0a for any given plane is widened by the 
fact that decreases in dive angle are in practice 
usually accompanied by decreases in airspeed. 

The preceding discussion suggests two alternative 
methods of correcting for sight misalignment at a 
given range, dive angle, and airspeeds: (1) direct 
adjustment of the sight, until flight and sight lines 
coincide; or (2) computer adjustment, i.e., changing 
Tc by a percentage tc determined from Figure 24. 

The adjustment required, however, depends in 
either case on the values of a and T^, and in case 
(2) on 5 as well. Since it is not feasible to make 
frequent readjustments of either type in any one 
plane, in practice a fixed adjustment must be made, 
such as would completely offset the sight error at 
some chosen intermediate or modal value of S, a, 
and V. At other values an impact error will gener¬ 
ally result, the magnitude of which depends on the 
method used — a fixed sight adjustment, a fixed 
computer adjustment, or some combination of the 
two. The most efficient method is, of cour.se, the one 
which minimizes this impact dispersion. 

The following example illustrates the results of a 
fixed computer adjustment: The sight installed in an 
F6F plane at nominal weight (12,400 pounds) is 
misaligned by —20 mils at slant range S = 7,500 
feet, dive angle a = 40 degrees, and airspeed V =350 
knots. A fixed per cent adjustment in Tc is made in 


an amount just .sufficient to offset the — 20-miI 
sight error at {S, a, F). cau.sing a hit. It is desired 
to determine the re.sulting impact error at slant 
range <Si = 12,000 feet, dive angle = GO degrees, 
and airspeed I^i = 375 knots. 

From Figure 24 the required per cent adjustment 
in Tc per mil at 7,500 feet, 40 degrees, and 350 knots 
(point T) is €<;/0 = 0.75 per cent per mil, so that for 
0 = —20 mils, the fixed adjustment is = —15.0 
per cent. In other words, under these conditions a 
15 per cent decrease in Tc, by itself, would displace 
the impact point by an amount equal and opposite to 
the displacement which would result from a —20-mil 
sight error alone. 

At another range, dive angle, and airspeed, these 
two displacements, while oppositely directed, will 
generally be unequal in magnitude, and in addition, 
the angle of attack will generally be different. Thus 
the impact error at (*Si, ai, IT) will be the algebraic 
sum of three displacement components: (a) the 
difference A0a between the angles of attack at 
(a, F) and (ai, T^i) is a change in sight error and 
therefore causes an impact displacement 5a; (b) the 
original sight error 0 = — 20 mils, by itself, would 
result in a positive (beyond-target) impact error 
5^; (c) the adjustment = —15 per cent, by itself, 
would give a negative (short-of-target) error 5c. 

1. The difference in angle of attack is determined 
from Figure 26. For an F6F plane at nominal weight, 
this nomogram gives 0a = 14.9 mils at a = 40 de¬ 
grees, F = 350 knots, and 8.5 mils (determined by 
extending line N and using lower extension scale 0) 
at ai = 60 degrees, IT = 375 knots. Hence, A0a = 
— 6.4 mils. But from Figure 23, at ai = 60 degrees 
and *Si = 12,000 feet (point Q), —b '4> = 14 feet 
per mil, so that the impact displacement due to 
change in angle of attack is 5a = 4-90 feet. 

2. From this same ratio — 5 0 = 14 feet per mil, it 
follows that the —20-mil sight error in itself causes 
an impact error 5^ = 4-280 feet. 

3. Finally, at 12,000 feet, 60 degrees, and 375 knots, 
the value of 5c/ tc may be read from Figure 25. As 
there defined, n = (375/350)^ = 1.148, so that at 375 
knots, 12,000 feet = (12,000 T.148)n = 10,450n feet. 
The point Q determined by this slant range and 60- 
degree dive angle lies between the curves marked 
lOn and 15n, slightly nearer the latter, so that 
approximately 8c/tc = 13n = 14.9 feet per per cent. 
The —15.0 per cent adjustment in Tc therefore dis¬ 
places the impact point by about 5c = —220 feet. 

The resultant impact error at (Si, ai, Fi) is then 



AIR RESISTANCE IN BOMB TOSSING 


127 


+ 5^ + 5, = + 90 + 280 - 220 = 150 feet, i.e., 
the bomb may be expected to fall 150 feet beyond the 
target under the given conditions. 

The effect of angle of attack variation may be 
seen to be of considerable importance. If were 
neglected in this example, (2) and (3) alone w'ould 
yield an impact error of + 60 feet, or only 40 per cent 
of that given in the above. Quite often even the 
algebraic sign of the resultant error is changed by 
this effect. 

According to the wording of the hypothesis, this 
example may at first appear to typify only the 
computer adjustment method. But if the original 
misalignment Avere given not as —20, but as —30 
mils, of which 10 mils were corrected by a sight 
adjustment and the balance by a computer adjust¬ 
ment, the solution Avould be identical, yet the prob¬ 
lem would appear more general, involving a combi¬ 
nation of sight and computer adjustments. Further 
details are in reference 101 . 


5 AIR RESISTANCE IN BOMB TOSSINQi ^s 
6.5.1 Trajectory Equations in Air 


The study of air resistance effects is facilitated by 
utilizing a coordinate system consisting of horizontal 
and vertical coordinates i and ?? with origin at the 



FiGUREi27. Flight and trajectory diagram of toss 
bombing maneuver, showing t) coordinate system and 
three trajectories: solid curve PH\ tlieoretical vacuum 
trajectory through target H) dashed curve P'K': air 
trajectory with same release conditions; dashed curve 
P”PI : air trajectory from release point so determined 
as to produce hit. 

point of release as indicated in Figure 27. In this 
figure the solid curve PH is a vacuum trajectory 
through the target at H, PH'K' an air trajectory 


vith the same release conditions, and P''H an air 
trajectory from a release point determined so that 
the bomb will hit the target. The percentage increase 
in Tc required to obtain the trajectory P"H is 

^ = (84) 

Tc VTc S OH ' 

The equations of the vacuum trajectory, using 
^,77 coordinates, are 

^ = u,{t - r,), 

and 

V = irp(f - 7V) + ho(t - T^y, (85) 
where Up and TFp are the horizontal and vertical 
components of velocity at release. If the coordinates 
of the target are Vh = v, elimination of the 

quantity t — Tp between equations (85) yields the 
relation 

^=I1px + _^X2. (86) 

Up 2uy 

The corresponding relation for the air trajectory 
PH'K' will now be obtained. If w = ^ and w = -q, 
then the velocity of the bomb in its path is 
V = Vm“ -b The retarding acceleration, a, due 
to the air, is assumed to be representable in the form 

a = Bv^, (87) 


where B is constant along the trajectory. The 
degree of accuracy of this assumption will be dis¬ 
cussed m Section 6.5.2. The components of the 
retarding acceleration are 


= Buv, 
Clr, = Bu'v. 


( 88 ) 


From equation ( 88 ) the equations of motion of the 
bomb are 


ii = — Buv, 
io = g — Bwv. 


(89) 


Let (j> be the angle between a tangent at any point 
on the trajectory and the horizontal, so that 


w 

taii(/) = u' 


(90) 


Differentiating both members with respect to t gives 


(sec-^)0 = 


which, by use of equation (89) can be reduced to 


</> = 


g cos (f) 

V 


(91) 

















128 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


Equating components of acceleration in the direc¬ 
tion of the tangent to the path gives the relation 

h = gr sin </) — Bv^. (92) 

Between equations (91) and (92) the quantity dt 
can be eliminated. This yields the relation 

dv Bv^ . 

— = V tan (/) —-, (93) 

d4> g cos 4> 

which is a differential equation for as a function of (p. 
While this differential equation can be integrated in 
terms of the elementary functions of mathematics, its 
solution in this form is quite cumbersome when it 
comes to making applications in numerical com¬ 
putation. For this reason the approximation 


B^B^--^, (94) 

cos (f) 

is made, in which ^ is a mean value of cf>. This 
approximation is quite good Avhen the total change in 
direction along the trajectory is not too large and 
when a (and hence (/>) is not too close to 90 degrees. 

With the use of equation (94), equations (89) 
become 

u = - Bv? sec 0 ,_ 
w = g — Buw sec 0 . 

integration of the first of equations (95) we have 


- —^ = Bit — Tp) sec 0 

11 Ur, 


r 


(9G) 


1 + BUpit — Tp) sec 0 

The use of this result in the second of (95) gives 
BUpW sec 0 


w = g 


whose solution is 


1 + BUpit — Tp) sec 0 


, _ 11 p + [git — Tp) + (1/2)BUp it — Tp)“ sec (/>] 
1 + BUpit — Tp) sec (f) 


(97) 


Equations (9G) and (97) give the components of 
velocity in terms of tune measured from the be¬ 
ginning of pidl-up and the conditions at release. 
Further integration gives the coordinates ^ and 77 
of the bomb after release in the form 


Ij-, p ^p) ~| 

B L cos (f) J 

, J, (, - T^y. + m) 

2 BUp sec 0 

^ Wp-gcos-^/i2JUp) ^ BUpit - 7^) 1 
BU p sec (j) L cos 0 J 


The elimination of the quantity t — Tp between 
these equations yields the Cartesian equation of the 
trajectory in the form 


w’here 

= _ 1 _ J- (g2Bf sec0_ |N 

B^ 2B‘'~e 

_ 2 i2B sec 0)^ 
for which an approximate formula is 


(99) 


( 100 ) 


6(|)^|B$sec0. (101) 

Equation (99) is seen to differ from ( 8 G) only in 
the term e(^) which is, therefore, the term due to air 
resistance. 


^ ^ The Constant B 

The quantity B, in reciprocal feet, will now be 
expressed in terms of the ballistic coefficient C. 
Modern ballistics tables are based on the Gavre 
function Giv), defined as the retardation of a pro¬ 
jectile of unit ballistic coefficient at velocity v. An 
examination of tables of Giv) shows that Giv) is very 
nearly proportional to v^ in the range of velocities 
used in bomb tossing. Thus, in the interval from 
350 feet/second to 800 feet/second the ratio G(?;)A^ 
decreases from 4.51 X 10“^ at y = 350 feet/second 
to 4.14 X 10“^ at ?; = GOO feet/second and then 
increases to 4.51 X 10~^ at v = 800 feet/second. 
The value 4.25 X 10“^ may be selected as probably 
the best value for this ratio, so that 
^-^5 X 10~ ^ 

“ C 


The Ground Error 


The ground error (5 = K'H in Figure 27) can now' 
be found by placing r] = v and = X — 5 in equa¬ 
tion (99). This gives 




or, making use of equation ( 8 G) 


0 = - + 
f V 




[- 2 x 54 - 52 + (X- 5)2e(X - 5)]. 

(102) 















AIR RESISTANCE IN ROMB TOSSING 


129 


In equation (102) the unknown 5 is obviously 
much smaller than X. Hence the term 5- can be 
neglected in comparison with the term — 2X5. In 
the same way, and by using equation (101) the term 
(X — 5)-e(X — 5) can be replaced by 
f5(X3 - 3X^5) sec 
Thus equation (102) becomes 
Q 


the value of the first fraction is taken from equation 
(44) and the value of the second from equation (106). 
This results in the formula 


Tr. 


sin « cos q; + dp [sin-a + V 1 + (l /p.) cos a] 

X 


0 = - -^ + 

U„ 2Up 

whose solution for 5 is 


Vi + (l/^) cos Oi 
BS 


(107) 


-f- 2X5 + fB(X3 - 3X25) sec (/)] 


5 = 


Bg\^ sec (j) 


3{Up\\ pT g\ -\-Bg\^ sec (j>) 

For use in bomb tossing this equation may be 
expressed in terms of the dive angle a, the velocity 
of the airplane V, the slant range S = VTc, the aver¬ 
age pull-up acceleration p, and the ratio r = Tp/Tc. 
For this purpose the following relations will be used: 


3[T/isina -b (1 + BS)dp] 

This formula gives the relative increase in Tc which 
will correct for air resistance. Formula (107) may be 
approximated to in a variety of w'ays. The approx¬ 
imation to be made here consists of the following: 

1. Finst take a = 35 degrees, K = 3, leaving the 
formula 


AT. 


^ (.5675 X 1.814 0p) X 


Up = V cos (« — dp) 


Wp = V sin (a — dp) 


10-5 s/C 


X = S cos a: — aTp cos a — ?/p sin a (p [ 


S 

= a— . 
C 


V- . 

Xp = —sm dp 

gn 

It is found that 
X = >8 cose 


2/p= — (1 — cos^ 

gn 


Sa^l — 


sin dp/2 cos {a — dp/2) 

’ 


cos a 


(104) 


1.2517 + (1 + BS)dp 

2. Next, take the B which remains in the formula 
to be (4.25/2) 10"^ = 2.125 X 10~®, and calculate 
the value of a for V = 500 feet/second and T. = 5 
seconds. Then calculate a for V = 500 feet/second 
and Tc = 20 seconds. The average of the two 


5 = ^BS'^dpCOS^a I 1 — T 


sin dp/2 cos (a — dp/2) 


X < r/Z sin {a — dp) cos (a — dp) 


-f- dp cos 


fi 

a 1 — r — 


sin (Op/2) cos (a — Op/2) 


(105) 


Op/2 


1 + OpBS cos a r 1 - r . co^ (<^ - »p/2) TV‘ 

J L dp/2 cos a J J 


A good approximation to 5 is obtained by replacing 
sin dp by dp, cos dp by unity, and discarding all terms 
of degree two or greater in the small quantities r and 
dp. This approximate formula is 

BS‘dp cos Q! 


5 ^ 


3[T/isino! -[-(IT BS)dp] 


(106) 


values thus found will be used in an approximate 
formula for ATc/Tc. 

It is found that when Tc = 5 seconds, a = 2.697 X 
10"^, and when T. = 20 seconds, a = 2.103 X 10"^. 
Consequently the value 


2.697 T 2.103 


10'^ = 2.4 X 10“ 


The Correction for Air Resistance is chosen for a. This gives as a rough formula 


By using formula (106) to calculate the horizontal 
range error caused by air resistance, the percentage 
correction ATc/Tc of T. which will secure a hit can 
be found. Writing 

ATc _ VATc ^ 5 
Tc 5 * .s’ 


^Tc ^ c, X 10"^ 
Tc~ ’ C ' 


(108) 


This correction differs slightly from the correction 
given in reference 140, because of a simplified presen¬ 
tation of the theory. Variations occur in the approx¬ 
imations for 5, starting with equation (105). 


























MATIIEMATICIAL ANALYSIS OF HOMH TOSSING 


130 


WIND CORRECTION AND 
TARGET MOTION 

Introduction 

In any consideration of the effect of wind or target 
motion on the boml) tossing maneuver, it is necessary 
to specify the tj'pe of course which is to be flown 
b}^ the aircraft. Two types of approach are ordinarily 
most useful, the collision course and the pursuit 
course. 

In the pursuit course the airplane flies in such a 
way as to kee]) the center of the sight on the target 
at all times. For a stationary target and under no 
wind the flight path will then be a straight line which 
is coincident with the collision course for this case. 
If wind is present, however, or if the target is in 
motion, the pursuit course will be curved. A collision 
course, on the other hand, will be a straight line 
characterized by the condition that the airplane, if it 
continues on this flight path, will ultimately collide 
with the target. 

Other types of flight paths may be obtained if, 
instead of a fixed sight, a lead-com])uting sight is 
used, i.e., a sight which if kei)t on the target ulti¬ 
mately results in the flight line differing from the 
.sight line by an amount sufficient to obtain a hit. 
All of these possibilities will be discussed in this 
.section. 


Collision Course 
in the Presence of Vi ind 

Figures 28 and 29 show the collision course ap¬ 
proach in the presence of wind or target motion for 
the case in which the wind or target motion vectors 
lie in a vertical plane containing the velocity vector 
V of the aircraft, assumed to be constant during the 
dive. In order to establish a collision course for a 
target initially located at Eo the pilot mn.st offset 
his aiming point by the angle <p from the center of 
the sight. In Figure 28 it is shown schematically 
that, if the wind speed does not vary with altitude, 
the angle (j> is constant as the target moves suc¬ 
cessively through points Eo, Ei, and E 2 at times 
t = 0, t = Ti, and t = T^. The line OEc is the 
collision cour.se, of length VTc, along which the 
airplane has the velocity V. The relative velocity 
between airplane and target is the vector U. 


Figure 29 .shows that target motion with velocity 
Vg is etjnivalent to a wind of velocity IF, provided 
IF = — Vg. Again the angle cf) is constant and is 
the same as in the target motion case. The time to 
target is Tg, although the collision course length as 


CENTER OF SIGHT 



TARGET VELOCiTYWg 


Figure 28. Diagram of collision course approach to 
moving target. (For details see text, Section 6.6.2.) 

measured relative to the ground is UTg. The rela¬ 
tive velocity U is also the resultant velocity in this 
ca.se. What was the dive angle a in the target 
motion case becomes the aircraft heading angle. 
Thus the equivalence between tai-get motion with 


CENTER bF SIGHT 



Figure 29. Diagram of collision course approach to 
station.ary t.arget in presence of wind. (For details see 
text, Section 6.6.2.) 

velocity Vg and wind with velocity IF = — Vg 
consists in: (1) the same offset angle, 0; (2) the same 
time to target Tg; (3) the same aircraft velocity F; 
and (4) the dive angle in the first case being equal 
to the aircraft heading angle in the second case. 










WIND CORRECTION AND TARGET MOTION 


131 


Accordingly, the wind correction sighting grids, 
described in Section 2.4 may be used for both target 
motion and wind velocities, provided the target 
velocity vector is reversed in direction. The theory 
involved in the construction of these charts will now 
be developed. 



Figure 30. Velocity vector diagram illustrating method 
of construction of wind correction charts. (For details 
see text, Section 6.6.2.) 


is located at the fixed point R in his sight, the flight 
path will be along the line ZT, which is the required 
collision course. The immediate objective is the 
locus of point R as the wind velocity vector varies in 
direction through 360 degrees. 

Several relations between the angles marked in 
Figure 30 will be useful. These are all obtained by 
projecting the vector W in various ways. By pro¬ 
jecting W onto OZ a length equal to ^ or W sin f 
is obtained. By projecting onto OZ the components 
W cos and W sin 12 on the X' and Y axes respec¬ 
tively and adding these projections, the result 
W cos 12 cos a is obtained. (The projection of 
W sin 12 on OZ is zero.) It follows that 

sin f = cos 12 cos a. (109) 

In the same way by projecting first IF and then its 
components onto OX the relation 

cos f cos 0 = cos 12 sin a (HO) 

is obtained, and similar projections onto OY result in 
cos f sin 0 = sin 12. (Ill) 

Again from Figure 30, it is seen that 
^ = OR = OS + SR = IF cos f -f- ST tan0 

= IF cos r + ^ 

whence, solving for r, 


IF cos f 



The matter of dimensions is ignored here. 
But by equation (109) 

ST = W sin f = IF cos 12 cos a. 

Hence 


1 — w cos 12 cos a ’ 


Referring to Figure 30, let IF be the wind velocity, 
assumed horizontal, referred to the ground, and 
let V be the airplane velocity relative to the air 
mass. The plane X'Y' is the horizontal plane of the 
ground and OZ' is vertical. The airplane is in the 
plane of X' and Z', headed along the direction ZO 
with a velocity V so that this direction coincides 
with the center pip of the sight reticle. However, 
the wind causes the airplane to follow a flight path 
along the direction of the resultant velocity. The 
plane of X and Y is normal to the aircraft’s heading 
and hence constitutes a plane parallel to the sighting 
plane of the reticle. If the pilot flies so that the target 


where w = IF/F. Solving equations (110) and (111) 
as simultaneous equations for the angles f and 12 
gives 

tan 12 = sin a tan 6 

sin a 

cos f = . — (113) 

V cos^ 6 + sm^ a sin^ d 

By means of equation (113) equation (112) can be 
expressed in a form free of f and 12, namely, 

IF sin a 

V cos^ d + sin^ a sin^ 0 — co cos a cos 6 
This is the polar equation of the locus of R. 


















132 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


On clearing equation (114) of fractions, and using 
the relations x = r cos 6 and y = r sin 6. The equa¬ 
tion becomes 

V sin^ a — cox cos a = IF sin a, 

which can be put into the form 

( W CO sin a cos a 

X — - 

1 — co^ COS^ a 

lF=^sin^c^ ~~ ' IF^ “■ 

(1 — co^ COS^cc )- 1 — co^ COS- a 

Equation (115) is recognized as the equation of an 
ellipse for each set of values of IF, F, and a. One of 
these ellipses is shown in Chapter 2, Figure 20. 

When X and y are nondimensional, say in mils, 
then the ellipses are functions of the nondimensional 
parameter co. This is what makes possible the plotting 
of ellipses with co as the only variable. Equation 
(115) assumes the nondimensional form if all IF’s 
are replaced by co. 

Several remarks of interest can be made from 
suitable interpretations of either equation (114) or 
(115). Among these are the following: 

1. Since co^ cos^ a« 1, the major axes of the 
ellipses are nearly proportional to IF, while the minor 
axes are shorter than the major axes by the factor 
sin a. 

2. For very small co, that is, small wind velocity, 
the center of each ellipse is near the origin. 

3. For small positive a the ellipses are narrow, 
extending along the x axis, while for large a, they are 
nearly circular, the radius varying but little from IF. 



* * * ^ Ground Error 

in a Collision Course 

A study of Figure 28 shows that the collision 
course which is established is such that the bomb 
director will cause the bomb impact to be at the 
point Ec. Let 0 be the point where pull-up is ini¬ 
tiated and Te the pull-up time plus the time-of-fall 
of the bomb. At time the target w'ill be a distance 
VgTe from Eo, but the bomb Avill strike at point Eg. 
Hence the ground error in a collision course approach 
is 

K= Fe(n- G). (116) 

Using equation 11 of Chapter 2 as a source of Tg 


and approximating to the trigonometric functions 
in the usual way, it is found that 


r 

/ 1 1 

1 + 

U 1 -j-cos a 

M J 


g CO 

or, by making use of equation (4) of Chapter 2 

Tg = ["l + ^ i 1 + Vl + — cos ail 

L cos a { ^ y j J 


= T, 


K + V K (K — cos a) 


(117) 


Using the xpi function as a means of expressing Tp. 
this becomes 


Tg ^ 7v + V A ( A co s g) ^ ^ 

A + V K- - K cos a 

wdiere 

_ A' + V A (A — cos a) i/'i 
A + V”/C2 _ K cos a ■ 

In terms of n, equation (118) becomes 

5, = (1 - n)VgTg. (119) 

Values of 1 — n are given in Table 12 and show'n 
graphically in Figure 31, both based on A = 3. 



Figure 31. Curve.s for determining horizontal impact 
error dg resulting from collision course approach with 
wind or target motion. (1 — n) = (Sc/VgTg) versus a 
for different values of Tg/V] R = 3. 


These show that for a > 12 degrees, the bomb goes 
over the target. The use of Table 12 and equation 
(119) permits an easy determination of the range 
error. For example, if a = 30 degrees, V = 500 
































WIND CORRECTION AND TARGET MOTION 


133 


feet/second, and TdY = 0.03, the table gives 1 — n 
= 0.104. Assuming Vg = 50 feet/second, equation 
(119) gives 

8c = 0.104 X 50 X 15 = 78 feet. 

To obtain a hit under collision course conditions 
it is necessary to reduce the lead angle 0 or to change 
operation of the bomb director so that it will com¬ 
pute a release time dependent on the target or wind 
velocity. An analysis of this problem is given in 


In Figure 32, let (R, a) be the polar coordinates 
of the airplane during the dive, these coordinates 
referred to an origin at the target H. The angle 0 
is the angle between the sight line, which is along 
the radius R, and the flight line, which is tangent 
to the resultant velocity vector U. Thus at each 
instant the airplane is pointed along R at H but 
moving along a path making an angle 0 with R. 

Equating expressions for components of velocity 


Table 12. Values of (1 — n). 


a ^ 

0.01 

0.02 

0.03 

0.04 

0.05 

0° 

- 0.006 

- 0.026 

- 0.066 

- 0.139 

- 0.284 

10° 

0.012 

0.013 

0.002 

- 0.023 

- 0.069 

20° 

0.031 

0.062 

0.058 

0.058 

0.050 

30° 

0.047 

0.081 

0.104 

0.121 

0.131 

40° 

0.064 

0.110 

0.144 

0.171 

0.193 

50° 

0.079 

0.136 

0.179 

0.213 

0.241 

60° 

0.094 

0.159 

0.208 

0.247 

0.280 

70° 

0.106 

0.178 

0.232 

0.275 

0.310 

80° 

0.116 

0.194 

0.250 

0.292 

0.331 


reference 5. The equation for the release time when 
flying a collision course in the presence of wind or 
target motion characterized by the lead angle 0c is 
given by 


-[(- 


f)'-.] 

[-( 


X 


K + sin a tan 0, 


:)'] 


where 


V (sin a sin 0c + K cos 0c) 
fig sin (a - 0c) 


In this formula 0c is positive if U is above V; that is, 
Ve is in a direction opposite to that in Figure 28. 


Pursuit Course Approach^i 


yields the equations 

-i?: = V + TFcosa, R—=W sin a. (120) 
dt dt 

Elimination of the quantity dt by division results in 

the differential equation 

dR / cos a , \ , 

-- = ( - cot a ]da, 

E \ CO / 


{R,«<) 



Figure 32. Instantaneous vector diagram for pursuit 
course approach. (For details see text, Section 6.6.4.) 


For this type of approach the pip in the center of 
the sight is kept fixed on the target. It will be shown 
that in the presence of wind the flight line is curved, 
so that the dive angle varies with time. 


where co = W/V. This differential equation is easily 
integrated to give 

A 


R = 


sin a (tan a /2)i ’ 


( 121 ) 

















134 


iVIATHEMATICAL ANALYSIS OF BOMB TOSSING 


where A is the constant of integration, which may be 
determined by conditions at the first altitude point. 
The relation (121) is the polar equation of a spiral 
resembling a logarithmic spiral. 

From equation (120) the expression for (f) is 
obtained. 


— Rda T1 sm a oj sm a 

tan (p = - = -;- = -. 

dR V + W cos a 1 + w cos a 

( 122 ) 

Since a varies during the timing run, it follows that cf> 
will vary. The amount of variation in a will now be 
determined. 

Using the subscripts 1 and 2 to designate values 
at the beginning and end of the timing run, and 
making use of equation (121) the following relations 
are obtained: 

6 _ hi _ Ri sin ai _ /tan a 2 / 2 \A 
5 hi Ri sin Vtan ai/2/ 


It follows that 


Writing 


tan ai/2 
tan ai/2 


( 1 . 2 )“. 


«2 

tan — = tan 
Z 





(123) 


tan (ai/2) + tan ( 0 : 20 : 1 / 2 ) 

~ 1—tan(Q;i/ 2 )tan[(o; 2 —ai)/2] ’ 

substituting into equation (123), and clearing of 
fractions, a linear equation for tan [( 0 : 2 —o:i)/2] results. 
The solution of this linear equation is 


0:2 — ai 1 . (1.2)“ — 1 

tan -- = 4smo:i -. 

2 (1.2)“ .sin^ ai/2 + cos^ o:i/2 

(124) 


Since the right-hand member of equation (124) 
increases when co increases, and since the largest 
value of CO due to wind is about 0.25 (IF = GO knots, 
V = 240 knots), it can be asserted that 


tan 



< ^ sin ai 


( 1 . 2 )‘ - 1 

(1.2)* siiFo;i/2 + cos- 0 : 1/2 


< i sinai[(1.2)* - 1] 


0.0467 . 

-sm 0 : 1 . 

2 


Hence 0:2 — 0:1 < 0.0467 sin 0 : 1 . Taking 0:1 = 60 de¬ 
grees as the largest dive angle to be used, it is found 
that a 2 — «i < 0.0405 rad < 2.4 degrees. Conse¬ 
quently the change in dive angle between the first 
and second altitude points is negligible. 


^ ^ ^ Ground Error 

in a Pursuit Course 

Figure 33 is a diagram of the timing run while 
flying a pursuit course (Ri, 0 : 1 ) and (Ri, 0 : 2 ) being the 
polar coordinates of the two altitude points referred 
to H as origin. The pull-up is assumed to begin at 
the second altitude point. The velocity of the air¬ 
plane during pull-up is the constant resultant 
velocity U. 


y' 

/ 



Figure 33. Flight diagram of timing run (first to second 
altitude) for pursuit course approach. (For details see 
text, Section 6.6.5.) 


Let Tc be the time to target indicated by the 
altimeter. With this time to target the bomb 
impact would be at point H' if the dive angle gyro 
measured the angle a'. However, the dive angle 
actually measured is 0 : 2 , and since 0:2 > a', the bomb 
impact will be at J, somewhat short of H'. 

Identifying JH' with the error caused by an error 
in measuring a (and hence equation (49) gives the 
relation 


i = L ~ i a'-aa 

S b Tpo h \p h da ip 

The instrumental \p design function is very nearly 
linear for a > 20 degrees, and its rate of change is 
such that d\p/da = — 0.726. Also by equation (122) 

a' — ai = — 4>i = — CO sin a. 


Hence 


JH' ^ 0.726 CO sin a 


Taking the case a = 40 degrees, Tc/V = 0.028, 
it is found that = 0.643 and h = 3.9, so that for 
this case JH'/S ^ 0.19co, and JH/S^ 0.81 co. For 



















135 


W IND CORRECTION AND TARGET MOTION 


the same case it is found from equation (119) that 

^ = (1 - n)co = 0.14co. 
o 

Thus in this typical case the ground error is about 
six times as great with the pursuit course approach 
as with the collision course. 

* ^ ^ Automatic Range ind 
Correction 

Both the collision course and the pursuit course 
approaches require either a prior knowledge of, or 
some method of estimating, the magnitude and 
direction of the wind if a hit is to be obtained under 
wind conditions. For a collision course maneuver an 
appropriate sight-offset angle must be estimated. 
For a pursuit course approach the bomb release time 
must be changed by an amount dependent upon the 
magnitude and direction of the wind. It is seen that 
these methods burden the pilot with some additional 
duty and provide only approximate solutions to this 
problem. WTiat is desired is an instrumental tech¬ 
nique which automatically computes the desired 
wind correction and sets it into the bomb director. 

Of the type of automatic wind correction pro¬ 
cedures under consideration, two may be mentioned. 
( 1 ) The use of a lead-computing sight which attempts 
to place the aircraft on a flight path involving the 
proper lead angle, and hence is of the nature of a 
collision course method of attack; and ( 2 ) the use 
of a rate-of-turn gyro or pitch gyro to measure the 
rate of change of dive angle during a pursuit course 
approach. The voltage output of the gyro is a 
function of the wind velocity and may be used to 
decrease or increase the no-wind bomb release time 
by the amount necessary to obtain a hit. Method (2) 
w'ill be considered in Section 6.6.7, and method (1) in 
Chapter 8 . 

^ ^ ^ The Release Time 

for a Pursuit Course Approach 

In Figure 33 the X'OY' coordinate system corre¬ 
sponds to the one commonly used in the analysis 
of the bomb tossing maneuver. Here, however, the 
XOY system is appropriate. The path of the bomb 
after release is given by the equations 
X = Xp^ U{t- Tp) cos (Op + (1)2) + hg (t - Tp)^sma 2 , 
y = Vp + U (t — Tp) sin (0p+ 02) — Tp)^eosa 2 , 

(125) 


Avhere dp is the pull-up angle as measured in the 
X'O'i ' system and .Tp and xjp are the coordinates of 
the release point in the XOY system. 

If Xp and yp are the coordinates of the release 
point in the A'^OF' system, then 


and 


— sm dp , 

ng 


yp = —{I - cosdp), (126) 

ng 

and y. = K — cos a' = K — cos 0 : 2 . The equations 
connectmg the coordinates of the release point are 

Xp = Xp cos 02 — yp sin 02 , 

and 

yp = Xp sin 02 + tjp cos 02 . 

The slant range i ?2 = OH is given by 
i ?2 _ sin (o !2 — 02 ) 

UTc sin 0:2 


(127) 


(128) 


The immediate problem is to combine the preceding 
equations of this article, together with the conditions 
for a hit, namely x = R 2 , y = 0, so as to get an 
expression for the pull-up angle dp in terms of the 
measured parameters. 

The first step is to express Xp and xjp in terms of dp 
by combining equations (126) and (127). This 
results in 


Xp= — [sin {dp + 02 ) — sin 02 ], 

yg 


yp= -[cos 02 - cos {dp + 02 )] . 

ng 


(129) 


Next, in the second equation of (125) place y = 0, 
use the second equation of (129), and write Tj in 
place of t — Tp. This gives a quadratic equation for 
Tj , whose solution is 


U sin {dp + 02 ) 

If = --- ( 

yg cos a 2 


j 2 cos 0:2 [cos 02 — cos {dp -f 02 )] 


Placing this expression for Tj into the first equa¬ 
tion of (125), at the same time using the first equation 
of (129), and replacing x by the value of 7^2 as given 









136 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


by equation (128) results in an equation which can 
be written 


(j sin ai sin^ {dp + <^ 2 ) o’ sin {Bp + <^> 2 ) cos {dp + 4 > 2 ) 
cos^ q !2 cos ai 

+ sin {dp + (^2) — cos {dp + <^2) 
cos 0:2 

^ sin (0:2 - 02) _ UgTc sin {a^ - (ki) _ ^ 
cos a2 U sin 0:2 


In order to solve this equation comfortal)ly for dp 
certain approximations are made, the first of which 
is in the expression for a. In this expression replac¬ 
ing cos 02 — cos {dp -b 02 ) in the numerator by 
1 — cos {dp 02 ) increases the expression slightly 
and permits it to be reduced to 


0- = M + 


/, ,2 cos 

^ V1 + —r-' 


_ 1 _ 

1 -b cos {dp + 02 ) 


Next, replacing cos {dp + 02) by unity decreases the 
expression slightly. Hence the expression 


■ = M 


1 

1 + — COS a2 = M + 
M 




+ cos a^), 
(131) 


which may be compared with the corresponding 
expression in Chapter 2, is an excellent approxima- 
tioai to (T for all values of 02 and dp which occur in 
bomb tossing. 

The next two steps are to replace cos {dp + 02) 
by 1 — I siiT {dp + 02 ) and to omit the resulting 
term of degree three in sin {dp + 02). This leaves the 
quadratic equation (132) for sin {dp + 02), 


sm a 2 
coso;2' 


(— -1- - —^ sin- {dp + 02 ) + ("l +-'j 

\2 cos a2/ \ COS 0:2/ 


X 


sin {dp + 02 ) — 


sin 0:2 — sin ( 0:2 — 02 ) 
cos 0:2 


= (132) 

U sin 0(2 


The solution of equation (132) for sin {dp + 02 ) is 


On placing 02 = 0 , equation (133) gives the pull-up 
angle dj which will cause the bomb to land at J; 
that is, 


sin dJ 


where 


figTc 2 cos 0(2 

U[K + V/v+A' - cos« 2 )] * 1 +Vl + 2lSj ’ 

(134) 


= 


JigTc sin 

ml 


Since 02 is small, it is clear that dp = dj — C02, 
where C is nearly equal to unity. The value of C 
can be calculated in a particular case by calculating 
dp + 02 from equation (133), 0/from equation (134) 
and then using the defining equation C = {dj— 0p)/02. 

The fact that the difference between dp and dj is 
nearly equal to 02 means that the correct pull-up 
angle, which will secure a hit when making a pursuit 
course approach, is obtained by subtracting from 
the pull-up angle dj (normally determined by the 
bomb director) an angle nearly equal to 02. This 
can be interpreted in terms of the so-called theory 
of the rigidity of a trajectory in exterior ballistics, 
since the main part of the correction necessary to 
cause a hit at H is merely the rotation of the tra¬ 
jectory through an angle of size 02 . 


Instrumentation 
of the Wind Correetion 

The wind correction term may be introduced on 
the first charging network of the computer, appearing 
as a charge which is either subtracted from or added 
to Tc according as 02 is positive or negative. That is 

_ Tc4' - E 

K + Va2 _ K' 

Since 


K + Va^ - K 


sin 0(2 — sin («2 — 02 ) ligTc sin (a 2 — 02 ) 


sin {dp + 02 ) = 


cos 0(2 


U sin « 


X 


2 cos 02 




A + Va(A - cos a2) '' 1 + Vi + 2 / 3 ^ ’ 

_ sin a2 sin 0:2 — sin (0:2 — 02) . P-gTc sin (0:2 — 02) 


(133) 


A 


X 


cos a 2 


+ ■ 


U sin ( 







































WIND CORRECTION AND TARGET MOTION 


137 


the value E should have is 

E = {Tj - Tp,) {K + 


= -{dj- 0p) (/V + VA'2 _ II) 

gn 


CUjH 

gn 


(K + Va'2 - K), 


(135) 


The relation between </)2 and the output from the 
rate-of-turn gyro will now be determined. The 
output of this gyro is merely the angle Aa. Following 
the procedure used in Section 6.G.4 it is possible to 
express Aa. in terms of 0 : 2 . From equation (123) the 
relation 

.L /i o\u.tan ( 0 : 2 / 2 ) — tan (Ao/2) 

tan — = ( 1 . 2 ) -—-— 

2 1+tan ( 02 / 2 ) tan (Ao/2) 

is obtained. Solved for tan (Ao/2) this relation 
becomes 

^ Ao (1.2)“ - 1 

tan — = -— 

2 ( 1 . 2 )“ + taiF ( 02 / 2 ) 


^ Ao (l/5)aj tan ( 02 / 2 ) 1 

tan — ^ - • = — CO sm 02 . 

2 , , , , 02 10 


1 + taiF - 
2 


Hence 


Ao = l/5co sin 02 . 

From equation (122) we have the relation 

. CO sin 02 

tan <p 2 = - 

1 + CO cos 02 

which becomes upon using equation (136), 

5Ao 


tan (/)2 = 


Since 

it follows that 


1 + CO cos 02 
t/ = T (1 + CO cos 02 ), 
5FAo 


tan 02 = 


U 


and hence equation (135) becomes 
CU 


(136) 


(137) 


E = —^ (A: -(- Va '2 — K) arc tan 

(/M _t 

^ 5CF(/v + V/^ - K) Ao 


5FAo 


(138) 


Some of the approximations made in the preceding 
discussion are admittedly crude. For numerical work 
recourse should be had to the exact equations. 


It is possible also to compensate for the wind by a 
fractional rather than an additive correction to the 
pull-up time. Thus, writing 

_ (1 - e) 

1 p</. — --- 


it is found that 

e = 


K -b VA2 - K 
Tj - E 


= . (139) 

Tj ^0 

The correction e show's less variation with dive angle 
than does E. 


6.6.9 Wind Compensation Using 
a Photoelectric Accelerometer 

When flying a pursuit course in the presence of 
w'ind it has been seen that the flight path is curved. 
Because of this curvature there e.xists an additional 
force on the accelerometer w'hich has not been taken 
into account in the preceding considerations. This 
force is in such a direction as partially to compensate 
for range errors due to wind. Thus, in a tail wind 
the path is concave dow'nward, and the centrifugal 
force is upward. The net force on the unbalanced 
mass of the accelerometer is reduced, corresponding 
to a larger dive angle. Therefore a reduction occurs 
in the value of the 0 function and a corresponding 
reduction in the release time computed by the bomb 
director. Conditions are just reversed in the case 
of a head wdnd, resulting in an increase in the com¬ 
puted release time. 

The object of Section 6.6.9 is a determination of 
the amount of compensation for w'ind effect provided 
by the use of the photoelectric accelerometer de¬ 
scribed in Chapter 8 . To this end the following 
quantities are calculated. 

1 . Radius of curvature p of flight path. 

2. Resultant centrifugal acceleration a. 

3. Corresponding change in dive angle and 0 
function. 

4. Resulting change in release time, ATp. 

5. Ep, the correction obtained from the photo¬ 
electric accelerometer, as given by equation (135). 

6 . EpIE, the fraction of the required correction 
which is obtained l^y using the photoelectric accel¬ 
erometer. 

7. E — Ep, the correction required from the rate 
gyro w'hen used in conjunction with the photo¬ 
electric accelerometer. 




















138 


MATHEMATICAL ANALYSIS OF BOMB TOSSING 


8. e — gp, the fractional correction required from 
the rate gyro when used in conjunction with the 
photoelectric accelerometer. 

Using the formula for radius of curvature in polar 
coordinates, 

p= __ , ( 110 ) 

R"- + 2 {(IR/day - R m/da^ 
and taking the value of R from equation (121) it is 
found that equation (140) gives 

i?(l + 2co cos a + co‘)^ 


P ~ 

CO (1 + CO cos a:) sin a 
The corresponding acceleration is 
^ _ F^co(l + CO cos a) sin a 

P 72 Vl + 2co cos ex + co“ 

Va (1 + CO cos a) 1 cx 


(141) 


Vl 4- 2co cos cx +co2 


Ji + ( Y 

' \ 1 + CO cos a/ 

(142) 

the expressions containing a being obtained by using 
the second equation of (120). To a first approxima¬ 
tion, a = Va. 

The net force on the unbalanced mass of the 
photoelectric accelerometer is 

F = mg cos a — ma = mg ^cos a - j. 

Designating by a" = a 5q: the angle indicated by 
the accelerometer, it follows that 

cos (a -f- ha) = cos a — ^ ^ 


/ CO sin a \- 

g\l + (-) 

\1 + CO cos a/ 


(143) 


This is the equation which determines ha. To a first 
approximation its solution, ])rovided a is not too 
small, is 

ha ^ -5^ . (144) 

g sin a 

The charge accumulated on the first capacitor is 
proportional to 

fTc/^ fTc5r -1 

^ Jo ~ ^Jo L ^ ^ ^ 


= Tc '/'(cx) + 


57 


da 


g sm a Jo 

Using —0.726 as the value of d\p/da, this gives 

T^^Pia) = ( 145 ) 

g sin a 

Hence the change in relea.se time resulting from the 
use of the photoelectric accelerometer is 
3.63 T^Acx 


AT, ^ 


g(K 4- V/v^ — K) sin a 


Consequently 
T^Acx 


3.63 
g sin a 


j Cp 3.63 7 
and — = 


Acx gTc-p sin a 


(146) 


(147) 


Since in the second equation of (147) the factor 
.sin a is multiplied by the function, it follows that 
the wind correction supplied by the photoelectric 
accelerometer varies much less with dive angle when 
introduced as a fractional correction than when used 
as an additive correction. This means that if the 
rate gyro correction also is introduced on a fractional 
basis, the amount of correction required from it, 
e — Cp, will be roughly independent of dive angle. 






















Chapter 7 

MATHEMATICAL THEORY OF ROCKET TOSSING 


7 » EMPIRICAL EQUATIONS 

FOR TRAJECTORY DROPS 
OF AIRCRAFT ROCKETS^ 

7 .1.1 Formulation of Equations 

Fitting CIT Data 

E mpirical equations are found for the trajectory 
drop data on five Navy rockets and two British 
rockets given in California Institute of Technology 

booklets.216-218 

The trajectory drop is the gravity drop from the 
effective launcher line in forward firing from an air¬ 
plane, the rocket being fired from a zero-length 
launcher, and is a function of slant range (distance 
from rocket ignition point to target), dive angle, 
plane velocity (true airspeed), and rocket propellant 
temperature. The change in the trajectory drop 
caused by a change in propellant temperature (at a 
given dive angle and airplane speed) is, however, 
practically independent of slant range for slant 
ranges larger than 1,000 yards. 

Examination of the graphs for the trajectory drops 
of the rockets indicates that a suitable general form 
of the empirical equations is 

ey = eo(a,Tp,To) + ti{a,R,Vp,T q) + i^e(ot,Vp,T), (1) 
where T is the propellant temperature, is the 
trajectory drop at propellant temperature T, R is the 
slant range, a is the dive angle, Vp is the true airspeed 
of the airplane, and Tq is a particular propellant 
temperature. The term eo{a,Vp,To) is the value of 
ey when R = 0 and at the particular temperature 
To] €i((x,R,Vp,To) is the increase in Mhen the 
range increases from 0 to R, the temperature remain¬ 
ing at To] and Ae (cx,Vp,T) is the difference between 
the trajectory drop at propellant temperature T and 
at T 0 . 

Taking To = 70 F, equation (1) was evaluated for 
the various rockets and then reduced by one term. 
The simpler form was possible because of a common 
factor in the first and third terms. For all rockets 
considered, the simplified empirical equations of the 

a Chapter 7 is appendix material to Section 2.2. 
b Section 7.1 was prepared by jNI. E. Rolfs of the State 
University of Iowa. 


trajectory drops at propellant temperature T are of 
the form 


€t = 


vRe-^r>'^+~h{T)\F{y). 




( 2 ) 


Table 1 gives the values of p, /S, r, and h{T) for each 
rocket considered. The superscripts refer to the 
reports listed in the bibliography giving the deriva¬ 
tions of the respective equations. In connection with 
this table, the units for the various quantities are as 
follows: T in degrees Fahrenheit, ey in mils, R in 
yards, y in degrees, Vp in knots, and the dimension¬ 
less function F{y) is graphically defined in Figure 1. 
This function is discussed further in Section 7.2.8. 


Table 1 


Rocket 

P 


r 

h{T) 

2.25-in. AR(Fast)>” 

0.060 

550 

0.25 

T^ — 2AQT + 11,900 

3.5-in. ARi ^2 

0.062 

550 

0.195 

T2 — 350^ + 19,600 

RP3, 3.5-in.i’' 

0.044 

500 

0.25 

jT^ —240r 4-36,900 

5.0-in. ARi'^'i^o 

0.082 

550 

0.195 

— 350r 4- 19,600 

5.0-in. HVAR'"'' 

0.033 

640 

0.22 

7^2 _ 264r 4- 28,730 

RP3, 5.0-in.i” 

0.063 

500 

0.25 

^2 _ 240T 4- 39,900 

11.75-in. AR 
(Pres, model) 

0.0573 

500 

0.25 

72 —240r 4- 31,900 


In order to show how well the empirical equations 
fit the data, graphs of corresponding values of the 
trajectory drops as determined empirically and from 
the CIT tables were made for small, medium, and 
large values of all variables involved. A typical case 
for the 5.0-inch HVAR is shown in Figure 2. These 
graphs show that the empirical equations, for useful 
values of the variables, fit the corresponding CIT 
data with about 3 mils maximum error and with an 
average error of 1 or 2 mils. 

For all rockets studied, the CIT tables give tra¬ 
jectory drop data for true airplane speeds of 200 to 
400 knots; propellant temperature of 0 F to 100 F; 
and dive angles of 0 to 60 degrees. The trajectory 
drop data for the 3.5-inch AR, 5.0-inch HVAR, and 
11.75-inch AR were given for ranges of 500 to 4,000 


139 














140 


MATHEMATICAL THEORY OF ROCKET TOSSING 


yards, whereas the data for the 2.25-inch AR (Fast), 
RP3 3.5 inches, RP3 5.0 inches, and 5.0-inch AR 
were only from 500 to 2,000 yards. Therefore, the 
degree of fit of the empirical equations for the latter 
four rockets depends upon the validity of extrapola¬ 
tions for ranges beyond 2,000 yards. 


7.1.2 Xhe Empirical Equations in 
Units Suitable for Theoretical Work 

In theoretical analysis, it is desirable to use feet 
instead of yards, feet per second instead of knots, 
and radians instead of mils. AVlien the variables are 




Figure 2. Trajectory drop e versus slant range R for different values of airspeed Vp, for 5.0-inch HVAR at temperature 
T = 70 F and dive angle a = 30 tlegrees. Solid curves are taken from tabulated experimental data at the tliree airspeeds 
specified; dashed lines are graphs of corresponding empirical equations, calculated from equation (2) and Table 1 of text 
It is seen that for R between 1,000 and 4,000 yards, error in empirical equation does not exceed 3 mils. 






























EQUATIONS FOR ROCKET TOSSING PULL-UP TIME 


141 


expressed in the foot-second system, equation (2) 
may be written 

€ = j /’(t) . (3) 

The values of the constants o, h, c, and of the func¬ 
tion h{T) are now those shown in Table 2. 


Table 2 


Rocket 

a 

h 

c 


h{T) 

2.25-in. .AR (Fast) 

2.0X 10-s 

930 

4.22 X 10-« 

7’2 

- 2407’ -I- 11,900 

3.5-in. AR 

2.07 X 10-5 

930 

3.30X 10-1 

7’2 

- 3507’ -1- 19,600 

RP3. 3.5-in. 

1.5X 10-6 

845 

4.22 X 10-< 

T-i 

- 2407’ -f 36,900 

5.0-in. AR 

2.7X 10-6 

930 

3.30 X 10-< 


- 3507’ -H 19.600 

5.0-in. HVAR 

1.1 X 10-5 

1,082 

3.72 X 10-1 

y.0 

- 2647’ -f 28,730 

RP3, 5.0-in. 

2.1 X 10-6 

845 

4.22 X 10-1 

Ti 

- 240r -1- 39,900 

11.75-in. AR 

(Present model) 

1.9X 10-6 

845 

4.22X 10-1 

7’2 

- 240r -f 31,900 


7 2 equations for rocket tossing 

PULL-UP TIME<= 
Introduction 

In the mathematical treatment of the problem of 
rocket tossing, it is necessary at the outset to make 
a decision regarding the inclusion of the various 
parameters affecting the pull-up time, such as time to 
target, speed of airplane, dive angle, type of rocket, 
type of airplane (angle of attack, launcher angle), 
temperature of rocket propellant, manner of release 
(zero-length launcher, lanyard firing), manner of 
pull-up, etc. The simplest procedure which can be 
expected to give theoretical results which can be 
compared with experimental results is one in which 
the following assumptions are made: 

1. The airplane dives, with constant velocity along 
a fixed straight line, directly toward a fixed target; 

2. The airplane pulls out of the dive with a spatial 
acceleration which is constant in both direction and 
magnitude, being perpendicular to the line of the 
dive; 

3. The rocket is released in such a manner that the 
initial direction of motion of its center of mass is the 
same as the direction of motion of the center of mass 
of the airplane; 

4. The axis of the rocket is always tangent to the 
path of the center of mass of the rocket — no yaw; 

5. The propellant is ignited at the instant of 
release. In general, the complexity of the ecpiations 

Section 7.2 was prepared by L. E. Ward, formerly of the 
State University of Iowa, now at Naval Ordnance Test 
Station, Inyokern, California. 


increases as more of the factors affecting the flight 
of the rocket are included in the discussion. 

In Section 7.2.1, equations describing the motion 
of the airplane during pull-up and of the rocket after 
release are set up subject to the assumptions listed 
in Section 7.2.2. No special assumption is made 
about the manner of variation of the magnitude of 
the spatial acceleration, K — cos a, of the airplane 
during pull-up, it being necessary at first only to be 
sure of the existence of certain integrals involving 
this acceleration. At appropriate points in the dis¬ 
cussion, which will be specially indicated, definite 
assumptions almut the manner of variation of this 
acceleration will be made. 

If this acceleration varies directly as U, r being 
a constant, then in general the equation which 
determines the pull-up time Tp is of degi’ee r -f 2 
in Tp}^^ It will be seen (see Section 7.2.11) that the 
effect of change in^'angle of attack can be included 
without raising the degree of this equation.^®® 
iMotion pictures of the action of an accelerometer 
during pull-up show that the spatial acceleration of 
the airplane increases nearly as the first power of 
the time.^®^ In this case, the equation for pull-up 
time is of degree three. Satisfactory approximate 
solutions of these equations of higher degree are 
obtained. 

When the spatial acceleration is replaced by a 
mean value, the equation for pull-up time reduced 
to a quadratic equation in Tp. It is shown that a 
useful approximation to the solution of this equation 
can be put into the form 

Tp = M/Fc + MdTd -h Mt, 
in which the first term is the only one which varies 
with the time to target Tc, the second term the only 
one which varies with the duration Ta of the delay 
period, and the third the only one which varies with 
propellant temperature. Each term varies wdth the 
velocity of the airplane during the dive, the dive 
angle, and the number of g’s present during pull-up. 
The second and third terms, respectively, show 
clearly the way in which a delay period and a change 
in propellant temperature affect the pull-up time. 

722 Assumptions 

The general assumptions which hold throughout 
Section 7.2 are listed here. 

1. The sight line and the flight line are fixed in 
space and pass through the target. 











142 


MATHEMATICAL THEORY OF ROCKET TOSSING 


2. During pull-up and until the ignition of the 
rocket propellant, the spatial acceleration of the air¬ 
plane is in direction perpendicular to the line of dive. 

3. There is a delay period between the release of 
the rocket and the ignition of the propellant. 

4. The rocket is launched so that the path of its 
center of mass at release has the same direction as 
the line of flight of the airplane at the instant of 
release. 

5. Upon release and at each instant thereafter, the 
axis of the rocket is tangent to the path of the center 
of mass of the rocket. This is the same as assuming 
that the rocket does not yaw. 

6. The target is stationary. 

7. The velocity of the airplane is constant during 
the dive. 


^ Notation * 

Figure 3 is a sketch showing in grossly exaggerated 
form the principal lines and angles associated with 
the path of the airplane during pull-up and the flight 
of the rocket after release. 



Figure 3. Diagrammatic representation of rocket toss¬ 
ing maneuver. 

0 is the point where pull-up began; the x axis is 
the line from 0 to the target; the y axis is upward 
and perpendicular to the x axis at 0. Tp is-the time- 
of-flight from 0 to the point where the rocket is 
released; Td is the time it takes the rocket to go 
from the release point to the ignition point D; 
Tc = OFIV, Avhere V is the velocity of the airplane. 
The line DL is tangent to the path of the rocket at 
the ignition point, da is the angle between DL and 
a line parallel to the x axis, a is the inclination of 
the line of dive to the horizontal. K is the number of 
^’s registered on an accelerometer at any instant 


during pull-up; K equals cos a during the dive, and 
K generally increases steadily during pull-up, tend¬ 
ing to reach a maximum if pidl-up is continued for 
several seconds. 

Unless specifically indicated to the contrary, all 
times are in seconds; distances, in feet; velocities, in 
feet per second; accelerations, in feet per second per 
second; angles, in radians; and temperatures in 
degrees Fahrenheit. 


The Equations of Motion 


During pull-up, the components of the spatial 
acceleration of the airplane on the coordinate axes 
are 

ir = 0 

y = (K — cos a) g. 

It follows that at the point of release, the compo¬ 
nents of velocity are 

Xp=V 

f^P (4> 

ijp = g K{t)di - gTp cos a, 

and the coordinates of the point of release are 


Vp — 


-/"[/: 


K{t)dt 


;1 dt - h 




gTp^ cos a. 


(5) 


By means of integration by parts, the expression 
for yp can be put into a form involving only single 
integrals, 

Up = 9 f (Tp — t) K{t)dt — IgTp^ cos a. (6) 


At the end of the delay period, the components of 
velocity of the rocket are 

Xd = V -L gTd sin a, 

fTp (7) 

K{t)dt — g{Tp -b Td) cos a, 


Vd = g 

JO 

and the coordinates of the rocket are 
Xd = V{Tp "T Td) + hoTd^ sin a. 
yd= - hg{Tp + Td)2 cos a 


( 8 ) 


+ g 


1J {Tp Td — t) K{t)dt. 
From equations (7), the angle 6d is given by 
J K{t)dt — (Tp -f Td) cos a 


tan Od = g' 


(9) 


V -F gTd sin a 
The path of the rocket after ignition is given by 






EQUATIONS FOR ROCKET TOSSING PULL-UP TIME 


143 


equation (3). In this application of equation (3), the 
slant range, R, is measured from the point D in 
Figure 3, and y is the angle a — 6,i 


The Equation for Pull-up Time 

If the rocket is to hit the target, the angles e, dd, 
5 of Figure 3 must satisfy the relation 

€ = + 5. (10) 

From this relation will be obtained the equation 
whose solution is the correct pull-up time. 

The angle e is given by equation (3); the angle da, 
by equation (9); and the triangle FHD yields 3 in 
the form 


tan 5 = —. (11) 

OF - Xd 


Instead of the exact expressions for dd and 3, their 
tangents as given by equations (9) and (11) are used. 
This approximation is considered to be acceptable 
since the trajectories of rockets are so flat that neither 
dd nor 3 ever exceeds 10 degrees, and since the radian 
measure of an angle less than 9 degrees never differs 
from its tangent by more than 1 per cent. Moreover, 
because of the flatness of the trajectory, it is satis¬ 
factory to replace R by IlF = — Tp — Td)V. 

On making these approximations and using equa¬ 
tions (8) and (9), equation (10) takes the form 


hF(y)A,{V)a\ - Tp - Td) + 


cF(y)h(T) 

9 


f: 


K{t)(U — {Tp Td) cos a 


1 + M 


( 12 ) 


+ 


J (Tp -b Td — t)K(t)dt — h {Tp + Td)‘^ cos a 


r. - 7’p - (i + m/s) 


Td 


where g = (g7bsina)/T",andthe function .42(F) is as 
defined in equation (31a), Chapter 2. If equation (12) 
is cleared of fractions by multiplying both members 
by the product 

(\. + - - (l + 


it is found that certain combinations of terms can be 


made and the resulting equations put into the form 

'-AA ny)AAY). 

+ ~ ^ F{y)h{T) - Tp - (^l-^ I^Td'j 

= "[n I ^ - fl + m)«] K{t)dt 

- {Tp + Td) ^Tc - Tp - cos a. 

(13) 

It is seen that the unknown, Tp, enters this equa¬ 
tion both algebraically and as the upper limit in the 
integral. Because of this fact, further investigation 
of the equation is restricted to several cases, each 
such that the integral in the equation can be easily 
evaluated and the resulting equation solved, at least 
approximately, for Tp. 


Lanyard Firing 

If a lanyard of effective length I is used to actuate 
the ignition mechanism, the propellant wall be ignited 
when the rocket is at distance I from the airplane, 
that is, when 

= {X - Xd)^ + (F - yd)\ 

where X and Y are the coordinates of the airplane 
at Tp + Td seconds after pull-up was begun. Ex¬ 
pressed by use of equations in Section 7.2.4, this 
relation becomes 

a Tp+Td \2 

{Tp+Td-t)K{t)dty 

(14) 

Equations (13) and (14) can be regarded as simul¬ 
taneous equations for the determination of the two 
unknowais Tp and Td- How'ever, this point of view' 
will not be followed up here. 

If ignition occurs upon release of the rocket from 
the airplane, it is only necessary to place Td equal 
to zero in equation (13), wEich is then the single 
equation for the determination of Tp. 

If in equation (14) a mean value K,n of K{t) dur¬ 
ing the delay period is used, that equation can be 











144 


MATHEMATICAL THEORY OF ROCKET TOSSING 


brought to a form easily solved for Td, resulting in 
the formula 




21 


' V KJ + sii: 


(15) 


It is noteworthy that Tp is not present explicitly in 
equation (15); it is present implicitly through /v,„. 
A good approximation to this result is obtained by 
omitting the sin^ a term and replacing by K^, the 
value of K when the propellant is ignited. This ap¬ 
proximate formula is 



^ Solution for Tp 

When a Mean Value of K Is Used 

If a suitable mean value K of K over the pull-up 


Bo = (1 + ,)F{y)A,{V)T,^ 

+ 1^2 cos a - (1 + m) T,T, 

- [cos a - (1 + F( 7 )A 2 (r)J T/ 

+ F{y)h(T) r 2T, - (2 + i,)Tj 

g L 

The form of solution of the quadratic equation (17) 
best suited to present purposes is 

T, =-. (18) 

Bi + V Bi“ — 4B0B2 

When the values of B 2 , Bi, and Bq are substituted 
into equation (18), the resulting expression is so 
complex as to be unmanageable. It is therefore 
necessary to discard the terms which have relatively 
little influence on the value of Tp. When this is 
done (for details of this step, see reference 176), the 
resulting formula is 


TcFiy)A 2 iV) -h 2Ticos « - F{y)A 2 {y)] A — F(y)h(T) 

7” =___ ^ -- - . 

^ K - cos a + F{y)A 2 (V) + V(K - cos a)[K - cos a + F{y)A 2 {V)] 


(19) 


period is used, a mean value theorem for integrals 
permits the integral in equation (13) to be written 

+ 2 

= K\t,T, + I T^Ti - v]. 

When this is substituted into equation (13), that 
•equation takes the form 

B2Tp^ - BrTp A Bo = 0, (17) 

where 

B 2 = (I - m)(/v - cos a) AHA n)Fiy)A 2 iV). 

Bi = 2 [K - cos a -f (1 -f m)F( 7 )A 2 (T')] T, 

+ ny)h{T) 

9 

-f 1^2 cos a A {K — cos a) 

- + ^^ F(T)A2(r)lT,, 


This formula is capable of being Avritten in an 
obvious way as a sum of three terms, Tp = McTc 
+ MdTd + d/r, in which each term shows how the 
factors of time to target Tc, delay time Td, and pro¬ 
pellant temperature T, respectively, affect the value 
of Tp. 


7.2.8 Function F(7) 

Equation (19) is not ready for use in calculating 
the pull-up time in a numerical case because of the 
prcvsence of the function F{y). Originally defined 
graphically (see Figure 1), tables of this function 
have been prepared and a representation of this 
function by means of trigonometric expressions has 
been obtained. The table and the trigonometric 
representation will be discussed first, and then the 
connection with the dive angle and the pull-up angle 
will be established. 

Values of F{a) given in Table 3 were taken directly 
from the graph in Figure 1. Certain of these values 
have been changed slightly so that the differences in 
the tabular values Avill be regular. 

Certain theoretieal reasons connected with the 



















EQUATIONS FOR ROCKET TOSSING PULL-UP TLME 


145 


approximate computation of rocket trajectories (see 
reference 215, pp. 25, 26) indicate that F(a) may be 
represented with satisfactory accuracy by either of 
the formulas 

- ^ -, cos a (1 — C' sin a). (20) 

1 + C sin a 

This -was found to be the case, the best value for C 
being 0.27 and for C', 0 . 2321 . 

The function F{y) in formula (19) depends for its 
value on Once has been determined, y = a — da 
is found by subtraction, and the graph or the table 


The resulting relation is 

^ F{c - ea)A^{Y). ( 22 ) 

In order to solve (22) for da, the first two terms 
of the Taylor’s series for F(a — da), 

F{a - e^) = f(«) - e^F'(a) + -, (23) 

are used. This is permissible since dd is known to be 
small (never exceeding 10 degrees) and since it can 


Table 3. F(a). 


a 


Radians 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

1.000 

0.997 

0.993 

0.990 

0.986 

0.983 

0.979 

0.975 

0.972 

0.968 

0.964 

0.1 

0.964 

0.960 

0.956 

0.952 

0.948 

0.944 

0.940 

0.936 

0.932 

0.928 

0.924 

0.2 

0.924 

0.920 

0.916 

0.911 

0.907 

0.903 

0.898 

0.894 

0.889 

0.885 

0.880 

0.3 

0.880 

0.875 

0.871 

0.866 

0.861 

0.856 

0.851 

0.846 

0.841 

0.836 

0.831 

0.4 

0.831 

0.826 

0.821 

0.815 

0.810 

0.805 

0.799 

0.794 

0.788 

0.783 

0.777 

0.5 

0.777 

0.771 

0.766 

0.760 

0.754 

0.748 

0.742 

0.736 

0.730 

0.724 

0.718 

0.6 

0.718 

0.712 

0.706 

0.699 

0.693 

0.687 

0.680 

0.674 

0.667 

0.661 

0.654' 

0.7 

0.654 

0.647 

0.641 

0.634 

0.627 

0.620 

0.613 

0.606 

0.599 

0.591 

0.584 

0.8 

0.584 

0.576 

0.569 

0.561 

0.553 

0.546 

0.538 

0.530 

0.522 

0.513 

0.505 

0.9 

0.505 

0.496 

0.487 

0.479 

0.470 

0.460 

0.451 

0.441 

0.432 

0.422 

0.412 


Approximate values of F'{a). 


a 

Radians 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

— 0.34 

— 0.34 

— 0.35 

— 0.35 

— 0.35 

— 0.36 

— 0.36 

— 0.37 

— 0.37 

— 0.37 

— 0.38 

0.1 

— 0.38 

— 0.38 

— 0.39 

— 0.39 

— 0.39 

— 0.40 

— 0.40 

— 0.41 

— 0.41 

— 0.41 

— 0.42 

0.2 

— 0.42 

— 0.42 

— 0.43 

— 0.43 

— 0.43 

— 0.44 

— 0.44 

— 0.45 

— 0.45 

— 0.45 

— 0.46 

0.3 

— 0.46 

— 0.47 

— 0.47 

— 0.48 

— 0.48 

— 0.49 

— 0.49 

— 0.50 

— 0.50 

— 0.51 

— 0.51 

0.4 

— 0.51 

— 0.52 

— 0.52 

— 0.53 

— 0.53 

— 0.54 

— 0.54 

— 0.55 

— 0.55 

— 0.56 

— 0.56 

0.5 

— 0.56 

— 0.57 

— 0.57 

— 0.58 

— 0.58 

— 0.59 

— 0.59 

— 0.60 

— 0.60 

— 0.61 

— 0.61 

0.6 

— 0.61 

— 0.62 

— 0.62 

— 0.63 

— 0.63 

— 0.64 

— 0.64 

— 0.65 

— 0.65 

— 0.66 

— 0.66 

0.7 

— 0.66 

— 0.67 

— 0.68 

— 0.69 

— 0.69 

— 0.70 

— 0.70 

— 0.71 

— 0.72 

— 0.73 

— 0.74 

0.8 

— 0.74 

— 0.75 

— 0.76 

— 0.77 

— 0.78 

— 0.79 

— 0.80 

— 0.81 

— 0.82 

— 0.84 

— 0.85 

0.9 

— 0.85 

— 0.87 

— 0.88 

— 0.89 

— 0.91 

— 0.92 

— 0.94 

— 0.95 

— 0.97 

— 0.98 

— 1.00 


for the F function then gives the value of F{y). The 
procedure to be used here is to solve approximately 
equations (9) and (19) as simultaneous eciuations for 
the two imknowns Tp and dd. 

A sufficiently accurate formula for dd is obtained 
by starting with the approximate relation 




l\F{y)A,{V) + 2Td cos a 


( 21 ) 


2 (K — cos a) 
obtained from equation (19). This is substituted into 
the right-hand member of (9), taken in the form 

^ (K — cos a) Tp — Td cos a 

dd = g - --• 


be assumed that the higher derivatives of F(oc) are 
small. The resulting relation, 


dd 


gTcAAV) 

2V 


[F(a) - ddF'(a)], 


yields the approximate formula for dd, 

dd = - 


2V 


1 + grric^) 


A,{V) 

2V 


(24) 


Substitution from (24) into the first two terms of 




















146 


MATHEMATICAL THEORY OF ROCKET TOSSING 


the right-hand member of (23) gives the formula for 

ny), 


F{y) 


F{a) 


1 + gTria) 


^2(7) ' 
27 


(25) 


mits the indicated integration to be carried out. The 
resulting equation is of degree r + 2 in Tp, and it 
can be put into the form 


2p 


r + 1 — M 
(r + 2)(r + 1) 


^ + 2 


-J^{2T,+ ^T,)T/ + ' 
r + 1 


From this formula it is seen that F{y) is chiefly 
a function of dive angle since the ratio of A2(7) to 



Figure 4. F( 7 ) versus a for two values of Tg (5 and 25 
sec) and for two types of rockets; V = 500 feet/second 
[based on equation (25) of text]. 


7 shows little variation on the interval 450 < 7 <700 
and since the term gTcF'{a) [Ao(7)/27] never ex¬ 
ceeds 5 in numerical value. Values of F'(a) are 
tabulated with those of F(a), and thus F(y) can be 


Tv 


2p 


r + 1 - M 
(r-f 2) (r-fl) 


rp r+2 

p 


+ 


(1 


calculated from formula (25). Graphs of F{y) against 
a for several values of Tc and two types of rocket 
are shown in Figure 4. 


+ (1 + i.)F{y)A.{Y)T,^ - B,'T, + Bo = 0, (27) 

where 

B,' = 2(1 + i.)F(y)A,{V)T, 

+ [2cosa - (1 + ^)*-^F{y)A^(V)]Ti 

+ ?^L±2i) F(7);i(r), 

g 

and Bo is the same as in Section 7.2.7. 

An approximate solution of equation (27) which 
is of value in rocket tossing theory is obtained as 
follows. For large values of Tc, at least, the impor¬ 
tant terms in the left-hand member of (27) are 

- Ml 7’/ + ' + B(t)Aj(T 07’^ 
r-fl 

If this expression is equated to zero, the resulting 
equation yields a value for Tp which can be regarded 
as a rough approximation to the correct value; this 
approximation is 

Tp, = [?^F(7)42(F)n]7TT. 


much more accurate expression for Tp can now 
be obtained by the following procedure. Let equa¬ 
tion (27) be written in the form 


T m)F(7)A2(7) V - B.'Tp -f 


V 

r + 1 


(27, -f MTrf) 


and substitute Tpo for Tp in the right-hand member. 
After omitting certain parts of the resulting formula 
which have little influence on the value of Tp, it is 
possible to write finally 


Solution for Pull-up Time 
When K = cos a -f pt^ 


The solution of equation (13) for Tp when the 
spatial acceleration of the airplane during pull-up is 
of the form y = pgf, where p and r are positive con¬ 
stants, will now be considered.^*® In this case 

K = cos a -f pf. (26) 

Substitution of the expression (26) into (13) per- 


Tp^ 



Fiy)A,iV)Tc+2(cosa- FA,)T, 


+ 




r+r 


(28) 


Formula (28) represents a useful approximate 
solution of equation (27) for any nonnegative value 
of r. If r is an integer, the quantity p can be replaced 
by a constant multiplied by a derivative of K. 

















































EQUATIONS FOR ROCKET TOSSING PULL-UP TIME 


147 


Thus, if r = 0, then p = K ~ cos a; li r = 1, then 
p = dK/dt; and generally, p = (1/r!) {dn^/df). 
By means of this relation equation (28) can be 
brought to the form 


approximated reasonably well by a linear function of 
time. 

When r = 1 equation (27) becomes the third de- 



where 


H=l- 




('•+1) 



-F(y)A^(\r)T 


1 

r+1 


As in Section 7.2.7 it is necessary to obtain an 
expression for F{y) in terms of the observable 
quantities. If the method used in Section 7.2.8 is 
applied to equations (9) and (28), formula (25) is 
obtained again. Thus to the degree of accuracy 
used in this method it makes no difference in the 
value of F{y) whether a mean value of K be used or 
K assumed to vary in accordance with (26). 

Tests have been made of the degree of accuracy 
possessed by formulas (25) and (29) as solutions of 
the equations for 6^ and Tp. This was done in numeri¬ 
cal cases by calculating F{y) by use of (25), and then 
Tp from (29) on the one hand, and on the other set¬ 
ting up equation (27) and solving it by Horner’s 
method. Of the corresponding values of Tp found in 
this way, no pair was found to differ by as much 
as 1.6 per cent.^*® 


gree equation 



,,(7’, + iip)- (1 + M)F( 7 M,(n]- 
Tp^ -Bt'Tp + B„ = 0. (30) 


Due to the fact that terms of degrees r d- 1 and 2 
in equation (27) are now both of degree 2, it is pos¬ 
sible to give a solution of (30) which has features of 
interest and, at least in form, is different from (29). 

Equation (30) can be Avritten in the form , 


Tr, = 


\ 


Bo — RiTp -f- ^ M 


3 pTp^ 


J>(n + -Y) - (1 + y)F(-,)A,(V) 


( 31 ) 


On referring to the values of Bo and Bi it is seen 
that from (31) a first approximation to Tp is 


Tpo = >(7)-42(10n . 

' P 


(32) 


The Case r = 1 

In this case K is a linear function of t, being given 
by (27) Avith r = 1. This is the most important case 


When this approximation is substituted into the 
right-hand member of ( 31 ), a better approximation 
to the value of Tp is obtained. After omitting rela- 
tiA'ely unimportant terms, the resulting formula can 
be Avritten 


Tr> 



F(y)AAy)Tp + 2(cosa-FA,)Tj + - F(y)h(T) 

L g J 

(l - ^«) - 


p-^F(y)A,{V) 

c 


(33) 


in rocket tossing theory since motion pictures of an 
accelerometer taken during pull-up show that the 
rocket is usually released Avhile the spatial accelera¬ 
tion is increasing, and that this acceleration can be 


It can be seen that if r is taken equal to unity in 
formula (28), the latter becomes identical Avith (33) 
except for the terms in F{y)A2{V) in both numerator 
and denominator. Since these terms are small in 
comparison Avith the terms from AV'hich they are 


^IP^ESTR I CTE 35 
































148 


MATHEMATICAL THEORY OF ROCKET TOSSING 


subtracted, it is concluded that formulas (28) and 
(33) will give essentially the same value for Tp in 
any numerical case which arises in rocket tossing. 

It should be remarked that the methods used in 
deriving formulas (28) and (33) are capable of numer¬ 
ous variations, especiall}^ as to the manner in which 
the various approximations arc made. Moreover, 
any approximate formula obtained l)}^ such methods 
must be tested as to its degree of accuracy before it 
can be used vith any confidence to obtain numerical 
results. 


7.2.11 Effect on Pull-up Time 

of the Change in Angle of Attack 
During Pull-np 


In forward firing of fin-stabilized rockets from 
zero-length launchers the rocket is freed from the air¬ 
plane after traveling about 1 inch on the launcher. 
Thus, relative to the airplane, it has a small velocity 
at release and the action of the airflow on the fins 
tends to align the axis of the round with the airflow. 
The degree to which the round aligns vitb the airflow 
is given Iw the factor. This factor is obtained 
from theoretical calculations by CIT and is given in 
their publications dealing vith the trajectory drops 
of rockets 

If the round is launched at an angle X with respect 
to the airflow, the end result of the motion during 
burning is the same as if the rocket had been launched 
along an “effective” launcher line without fin 
action.The angle between the airflow direction 
(flight line) and the effective launcher line is given 
by X(1 — /). The value of f is usually from 0.90 to 
0.95, and thus the rocket effectively leaves the air¬ 
plane in the direction of the flight line if the launcher 
Ime is not too far from the flight line. As an example, 
if the launcher is 3 degrees from the flight line at 
firing, the round will leave in a direction within 2 
to 4 mils of the flight line. 

During the pull-up the angle of attack of the air¬ 
plane increases in accordance with the formula^*® 


n = 


CxwK 


(34) 


where Ci and C 2 are constants for any particular 
type of aircraft, w is the weight of the airplane, Vi 
the indicated airspeed, and K the number of g’s regis¬ 
tered on an accelerometer. This fact operates to 
raise the launcher line through an angle somewhat 


larger than the change in direction of the flight line 
during the same period. 

Moreover, at the beginning of pull-up the flight 
line and the sight line usually differ slightly in direc¬ 
tion due to a deviation of speed or dive angle or 
both from the standard conditions as.sumed in setting 
the sight. These two factors cau.se small changes in 
the pull-up time. The equation for pull-up time will 
be .set up in a form which takes account of these 
factors and under the assumption that K obej's 
equation (26). 

In rocket and boml) tossing the sight line is ad¬ 
justed to be parallel to the flight line for a median 
value of dive angle, loading, and airplane speed, 
u.sually a high airspeed as obtains in a dive. Thus in 
the preliminary dive with the sight on target before 
the pull-up, the flight line is ])ointed toward the 
target at the median dive angle and airspeed, but for 
other flight conditions the flight line deviates from 
the target. The assumption is made in bomb and 
rocket tossing that the flight line is pointed toward 
the target, and thus there will be a possible mil error 
at the target equal to the angle between the flight 
line and the sight line. In the case of bombs this 
error is minimized by the use of high airplane 
speeds,and for rocket tossing this error is opposite 
in sense to another error (see Section 2.2.10). Thus 
we are justified in assuming the sight line and the 
flight line to be coincident. 


7.2.12 Equation for Pull-up Time 


Let the sight line at the beginning of pull-up be 
taken as the x axis, and let cr designate the angle from 
the X axis up to the datum line in the airplane. If 
a and Vi are “standard” values of dive angle and 
indicated airspeed respectively under which the 
sight line and the flight line during a dive have the 
same direction, and if a is the value of cr under these 
standard conditions, then from (34) 


CiW cos a 


- Co. 


In a dive under nonstandard conditions, the angle 
from the x axis up to the flight line is given by 
\2 

cos a — cos 


vr 


j cos a — cos a J . 


(35) 


Let /3 be the angle from the datum line up to the 
launcher line and / the launching factor. Then the 
angle from the flight line at release of the rocket up 







EQUATIONS FOR ROCKET TOSSING PULL-UP TIME 


149 


to the effective launcher line is y{r]p + /3), where 
7=1—/ and 

C\w . CiwpTp . 

Vp = —— (cos « + pTp ) - C 2 =- 

Vi^ 

Let Qp be the “pull-up angle,” that is, the angle 
through w'hich the flight line turns from the beginning 
of pull-up until the release of the rocket. This is the 
angle measured by the computer. Then the angle 
in radians from the x axis up to the effective launcher 
line is 

(36) 

1,000 J 1,000 

Let € be the angular drop of the rocket from the 
effective launcher line until the target is hit. From 
Chapter 2 , equation (31), 

' = - Tp) +±F(y)k{T). (37) 

If to expression (36) is added the angle 3 (see Fig¬ 
ure 3), given by 

tan 5 = - — -, 

VTc - VTp cos {a -v) 

the sum will equal «. 

Equations (4), (5), and ( 6 ) are replaced by 
Xp = V cos (a- — 7 ]) 

P9 


Vp = 


r+ 1 

and 

Xp = VTp cos (cf — rj) 


rp r+1 

1 p 


+ V sin (a — 77 ), 


Vp = 


vg 


(r + 2){r -b 1 ) 
It follows that 
Q ^Vp _ ^ ^ 

"" ~ Xp 1,000 


Tp “+ VTp sin ((T — 77 ). 


yg 

r +1 


- r+1 


+ V sin (a- — 77 ) 


V cos {a — 77 ) 


(T - V 

1,000 


pg 


(r + 1)F 


rp r+1 
- -f p 


and 
8 ^ 


Up 


VTc — VTp cos {a — 77 ) 


pg 


(r + 2 )(r + 1 ) 


TJ+2 + VT, 


(T — 77 

’ 1,000 


F(r, - Tp) 


where the approximations made consist in replacing 
tangents and sines of small angles by their radian 
measures, and cosines by unity. 

Using these expressions wdth (36) and (37) the 
condition for a hit becomes 


pg 


(r+ 1 )F 


m r+1 
i p 


+ 7 


r Ciwp 

Ll,000y7 


1,000 J 1,000 


pg 


+ 


(r + 2 )(r + 1 ) 


T/+2 + VT, 


(T - V 

’ 1,000 


V{T, - Tp) 


= ^F{y)A,(V)(T, - Tp) + ^J(y)h(T). 

Arranged in the standard form of an algebraic equa¬ 
tion for the unknown Tp, this relation is 


rp r + 2 _ 

I p 


... 

Lr + 1 l,000ri2j 


pg 

r + 2 

- yvCxwVT, . S F(7).4,(r)7’p‘ 

1,000 + 2 

- ^gF(y)A,{\r)Tc + cF(y)h(T) - yV 
+ I F{y)A^{V)T/ + cF(y)h(T)T, 




1,000 J 


- I T. 


+ 718-/77 


1,000 


= 0 . 


(38) 


It is now' assumed that the spatial acceleration of 
the airplane betw'een the beginning of pull-up and 
the release of the rocket is proportional to the time 
since pull-up began, i.e., r = 1 . With the abbrevia¬ 
tions 

ypCiwV 


82 = 


l,000i’r 


5i = 82 TC — yV 


iS + r? 


and 


5o — I Tc 


1,000 

g- + 7/3 — /77 

1,000 


equation (38) becomes the cubic equation 

i POT,^ - [hpgT, - igF{y)A,(V) - {J T/ 

- lgF(y)A^{V)T, + cF(y)h(T) + 6,1 T, 

+ ^F(y)A^(,V)T/ + cF{y)h(ryi\ - 5„ = 0. 

(39) 

On the basis of values for Tp calculated by solving 
equation (39) for a 5.0-inch HVAR released from an 

































150 


MATHEMATICAL THEORY OF ROCKET TOSSING 


FGF airplane under “standard conditions,” a = 35 
degrees and Vi = 320 knots, and for several values 
of Tc and T, it is concluded that for this combination 
of rocket and airplane the effect of change in angle 
of attack during pull-up on the computed pull-up 
time never exceeds 2 per cent and for most condi¬ 
tions is less than 1 per cent. The effect of a combi¬ 
nation of a deviation from standard dive comlitions 
of as much as 10 degrees and 40 knots and the in¬ 
crease in dive angle during pull-up on calculated 
pull-up time has been found to be nearly 4 pei’ cent 
for V = 310 knots, a = 25°, = 25 seconds, and 

T = 100 F. 

7 3 ROCKET TOSSING INTEGRATION 
ERRORS OF THE BOMB DIRECTOR 
WHEN PULL-UP ACCELERATION 
VARIES WITH TIMEd 

Introduction 

Determination of the accuracy of the integration 
performed by the ])omb director when pull-up accel¬ 
eration varies with time involves the comparison of 
data which represent the instrumental operation 
with the theoretical formula for a hit. It is assumed 
in this section that the acceleration acting on the 
airplane during pull-up is given by K = cos a + 'pt. 
This is a close approximation to the actual condi¬ 
tions during a rocket tossing pull-up. If the analysis 
were extended to include bomb tossing, however, 
allowance would have to be made for the fact that 
K may reach its maximum value before the bomb is 
released. This analysis attempts to take into account 
all the physical and electrical conditions to which 
the unit is subject and determine the accuracy with 
which the computer calculates the solution. The 
general approach and methods are summarized as 
follows: 

1. A formula representing the solution given by 
the computer was developed, taking into account 
the delay in integration until the value of K reaches 
1.3. Since both theory and experiment show that 
the K block will oscillate as it descends, this oscil¬ 
lation was included, but tests have shown that its 
effect is negligible; therefore, the unwieldy complica¬ 
tions introduced by oscillation will not be discussed 
here. 

d Section 7.3 was prepared by P. G. Hubbard of the State 
University of Iowa. 


2. A laboratory computer AN/ASG-10 (XN), 
Mark 1 Model 0, was modified to act as it would 
during pull-up. The linear increase in acceleration 
was simulated l)y having a small electric motor pull 
the K block down at a constant rate, starting at the 
end of the first timing period; the correct starting 
point, corresponding to K = cos a, was computed 
and set for each operation. A potentiometer was 
used to vary the voltage on the first condenser 
according to the theoretical calibration for the g 3 U’o 
(Mark 20 Model 00) to be used with the born!) direc¬ 
tor AN/ASG-10(XN),Mark 1 Model 0. The modi¬ 
fied unit was then tested l^y standard laboratory 
test equipment over the complete ranges of dive 
angles, in.strumental A factors, and times to target 
anticipated in rocket tossing flights. 

3. The results of lal^oratory measurements on the 
computer were compared with data from the derived 
formulas for several cases, and found to be in good 
agreement. A constant small difference was found 
to exist between the results for similar values of 
A, Tc, a, and p because of delaj'’ in the operation of 
relays and in the starting of the small motor. Addi¬ 
tion of 0.02 second to the re.sults of the formula was 
necessaiy to account for relay lag. 

4. The release time given by the laboratory unit 
was compared with the theoretical pull-up time for 
a hit using rockets. A simplified formula for pull-up 
time was used with the instrumental A taken as A 2 . 
In order to make the results represent more accu¬ 
rately the action of a computer in launching rockets, 
0.04 second was added to the release time given by 
the integrator, to make allowance for the delay be¬ 
tween firing of the thyratron and the moment at 
which the rocket actuall^^ leaves the airplane. 

The comparison shows that the instrumental 
pull-up time is too short at low dive angles, and 
slightly long for very high dive angles, especially at 
short range, ^\^len the instrumental A is very small 
(0.100), or/and at very short ranges (5 seconds to 
target), the instrumental pull-up time increases as 
the dive angle increa.ses instead of decreasing as it 
should. At average values of T^, A, and a as used in 
field testing with fast rockets, the instrumental and 
theoretical pull-up times agree very well. The dis¬ 
crepancies which exist are very noticeably reduced 
by increasing the value of p, which explains why a 
high pull-up rate has been found best in field tests. 

5. The computer circuit was modified in an at¬ 
tempt to make its results agree more closely with the 
theoretical times. The performance at low dive 





INTEGRATION ERRORS WITH VARYING ACCELERATION 


151 


angles with low g’s can be improved noticeably by 
shunting the rocket calibration condenser with a 
resistor. A value of 7 megohms (for the Mark 1 
INIodel 0 circuit) was found to give the best correction 
when the instrumental A is about 0.200. The opti¬ 
mum value experimentally agreed upon in field tests 
at Inyokern was 7.5 megohms. 

The items just listed bring out the fact that the 
eomputer does not operate perfectly when used in 
rocket tossing. The shortcomings which have been 
brought to light in this investigation have also been 
evident in field testing, and this investigation brings 
out the reasons for them. The adverse operation at 
short ranges, high dive angles, or low instrumental A 
is partly due to a lack of integration until K = 1.3, 
together with a K block which was designed prima¬ 
rily for use in bomb tossing. The revised \j/ card used 
in the Mark 1 Model 2 eciuipment will be of value in 
correcting both of these errors. 


Derivation of Formula for 
Instrumental Tp 


From Section 2.1.4 the voltage Vi built up across 
the first capacitor during the timing run is 


Vi 



(40) 


The second capacitor acquires charge in two dis¬ 
tinct steps. During the fir.st stage K < 1.3, and this 
capacitor is charged through a resistor of 10 meg¬ 
ohms. Since the length of this period is 


1.3 — cos a 
V 


(41) 


the voltage built up is Vo (1 — e 

At time h relays operate to change the second 
charging circuit so that the effective capacity of the 
second capacitor becomes 2A, and the resistance 
through which it receives charge is 10/ {K -f 
VA'- — A ). Consequently the charge present in the 
second capacitor at time tx is effectively 2Aco 
(1 — and it receives further charge as K 

becomes greater than 1.3 in accordance with the 
differential ecpiation 

''1 . = A- + VA-^ - A- 

2Ai;o - q 20A 


In order to facilitate the integration of the right 
hand member of (42) the function K VA- — A 
is approximated l^y 2.1053A — 0.8053. The error in 


this approximation is less than 1.7 per cent over the 
interval 1.3 < A ^ 3.5. Thus K + VA^ — A ^ 
at -f h, where a = 2.1053p and h = 2.1053 cos a 

— 0.8053, and equation (42) becomes 

dl. (43) 

2Avxx - q 20A 

The solution of (43) which meets the initial condi¬ 
tions t = tx,q = 2Avo(l — is 

q = 2A?;o{l - e-4/20A)qa(«2-(i2)+6((-<.) + A(ii \^ 

so that the instantaneous voltage across the terminals 
of the second capacitor is 

1-2 = ro(l - g-(i/20.4)qa((2-(.2) 

Firing occurs when V 2 = Vx. From (40) and (44) 
this is seen to occur at a time which makes the 
e.xponentials ec^ual, i.e., 

— _ JL. 

20 20A ’ 

Wa{tr — tx~) + h(t — tx) + Atx]. (45) 

The solution of (45) for f is the instrumental 
pull-up time T^. It is readilj^ found that this is 

-«.) + ((. + -Y. (46) 

^ a \ a/ 


Laboratory Testing 

A computer (Mark 1 Model 0 Director) was set up 
for standard laboratory testing with, however, the 
following additions. 

1 . The 4/ voltage was varied by means of a 
potentiometer. 

2. A small electric motor was attached so that it 
began pulling the A Idock down at the second alti¬ 
tude point with speeds corresponding to 1.08, 2.00, 
and 3.27 g’s per second. The correct starting point, 
corresponding to A = cos a, was computed and set 
by hand before each run. A relay between the J lead 
and ground on the computer completed the power 
circuit for the motor at second altitude and stopped 
the motor after firing of the thyratron. 

The effective \p value for each value of Tc was 
determined by measuring the output times at 150 
volts and reduced voltage, A and A remaining 
constant. The ratio of output time at to output 
time at 150 volts is the effective i/'. 

The instrumental pull-up time was measured for 
dive angles of 10, 20, 30, 40, 50, and 60 degrees; 
















152 


IVIATHEiMATICAL THEORY OF ROCKET TOSSING 


times to target, of 5, 15, and 25 seconds; instru¬ 
mental A factors of 0.101, 0.138, 0.238, and 0.350; 
and gf’s increase per second, p, of 1.08, 2.00, and 3.27. 

7.3.4 

Comparison of Laboratory Results 
with Computer Equation 

Figure 5 shows graphs of equation (46) and the 
instrumental Tp determined in the laboratory for 
similar values of A, p, and Tc. The effective values 
of \p determined from the computer were used in the 
equation (46). It is evident that the character of 
each set of curves is similar, but that the experimental 
values are consistently greater. The difference may 
be ascribed to delays in the action of relays and the 
starting of the small motor. A total delay in relays 


simplified formula 


\'A,F{y)Tc ( 

1 - 

V \ 

TeJj 


The pull-up time given by this formula can be com¬ 
pared with the integrator pull-up time if the instru¬ 
mental A is used in place of Ao. 




Figure 5. Comparison of theoretical rocket jmll-iip 
time Tp and instrumental Tp determined in laboratory, 
for typical values of A and Tc. Circles represent exper¬ 
imental points; unmarked solid curves and dashed curves 
are theoretical curves in nonoscillating and oscillating 
forms, respectively. 

and motor of 0.05 second is easily possible. The 
effect of oscillation of the 7v-block bob in an average 
case is shown by the dashed curve. 

^ ^ ^ Accuracy of Computer Solution 

Formula (28) becomes for the case of no-delay- 
period, no-temperature-corrcction, and r = 1 the 


Figure 6. Comparison of theoretical Tp with computer 
results, for several values of 77; *4 = 0.101, p = 2.00 
^/second. Solid curves represent theoretical Tp', points 
O and L represent Tp oi computer, without ancl with 
leakage resistance (7 megohms), respectively. 



FiGtTRE 7. Comparison of theoretical Tp with com¬ 
puter results, for several values of Tp, A = 0.350, p = 
2.00 fif/second. Solid curves represent theoretical Tp; 
points 0 and L represent Tp of computer, without and 
with leakage resistance (7 megohms), respectively. 


The representative graphs in Figures 6, 7, 8, and 9 
show how the pull-up times given by (47) compare 
with the instrumental pull-up times.An addition 
of 0.04 second has been made to the instrumental Tp 
because there is a delay of approximately that dura¬ 
tion between firing of the thyratron and the instant 
when the rocket actually leaves the airplane. The 
























INTEGRATION ERRORS WITH VARYING ACCELERATION 


153 


curves labeled L show the change in release time 
when a leakage resistance of approximately 7 megohms 
is put in parallel with the rocket calibration con- 



Figure 8. Comparison of theoretical Tp with com¬ 
puter results, for several values of Tc', A = 0.101, p = 
3.27 g'/second. Solid curves represent theoretical Tp-. 
points 0 and L represent T'p of computer, without and 
with leakage resistance {7 megohms), respectively. 

denser to improve the operation at low dive angles 
and long ranges. 

From the curves in Figures 6, 7, 8, and 9 the 
following conclusions are drawn. 



Figure 9. Comparison of theoretical Tp with com¬ 
puter results, for several values of Tc) A = 0.350, p = 
3.27 ( 7 /second. Solid curves represent theoretical Tp] 
points 0 and L represent Tp of computer, without and 
with leakage resistance (7 megohms), respectively. 

1. When the A factor or is small, the inte¬ 
grator does not solve correctly for the pull-up time, 
but gives a longer pull-up time for high dive angles 


than it does for shallow dives. This causes the 
rocket to overshoot if the dive angle is large and 
undershoot when the dive angle is small. For inter¬ 
mediate dive angles the two ciun'es agree very 
closely. 

2. When a very large .4 factor is used, the release 
time is too small except at very high dive angles or 
very short ranges. 

3. The curves emphasize the observation made in 
connection with field tests, namely, that a sudden 
pull-up is desirable. This corresponds to a large 
value of p, and bad the effect of minimizing the dis¬ 
crepancies. A large value of ?? does not necessarily 
lead to a large number of g’s because rockets are 
generally released before K reaches its maximum. 

7..?.6 Analysis of Discrepancies 

Formula (4G) permits an analysis to be made of 
the reasons for inaccurate operation of the bomb 
director when used for rocket tossing. A critical 
examination of the formula shows that the instru¬ 
mental Tp is influenced by three main factors. 

1. The term 2Ai/'T'c/a. This is the most important 
term; when the quantities in the formula are such as 
to make this the preponderant term, the action of the 
computer is satisfactory. 

2. The term h/a. This term is determined by the 
design of the iv-block resistance strip. 

3. The time b. This term represents the duration 
of the period before integration begins. 

When A, xp, or Tc is small, the term b takes on 
relatively more importance. It is this term which 
gives many of the curves in Figures 6 to 9 the in¬ 
correct slope. 

The explanation as to w'hy the pull-up times are 
too small at longer ranges or higher instrumental A 
values is to be found in the term b/a. The resistances 
in the K block were designed for bomb tossing. The 
graphs in Figure 10 show how this design is not ideal for 
rocket tossing because of the decrease in pull-up time. 

In Figure 10 the ordinates are proportional to the 
charging rate of the second capacitor, so that the 
total area under the curve is proportional to the 
voltage across the second capacitor. The solid 
curves give the theoretical rate for perfect integra¬ 
tion, while the dotted ones correspond to the rate 
in the present computer. These diagrams show why 
the release time is somewhat short for small dive 
angles and somewhat long for large dive angles. 














154 


MATHEMATICAL THEORY OF ROCKET TOSSING 


The same effects are shown m the earlier graphs in 
this section and have been observed in accurate 
analyses of field data. 



Figure 10. Comparison of theoretical (solid lines) and 
instrumental (dashed lines) charging rates of secondary 
condenser; both plotted as functions of time T for differ¬ 
ent values of a, with A =0.138 and p = 2.00 (//second. 
Shaded areas are proportional to voltages necessary for 
firing if Tc = 10 seconds. (Note difference in time Tp 
required to attain this area at theoretical and instru¬ 
mental rates.) To = time at which area under both 
curves is equal. 


74 EVALUATION OF THE A FACTOR® 
Introduction 

Theoretical curves for the A factor as a function 
of plane speed are given for the following rockets: 

®Section 7.4 was prepared by I. II. Swift, formerly of the 
State University of Iowa, now at Naval Ordnance Test 
Station, Inyokern, California. 


5.0-inch AR, 3.5-inch AR, 2.25-inch AR (fa.st),. 
5.0-inch H^^4R and 11.75-inch AR. The theoretical 
A factors are compared with experimental values 
determined by field tests and then new A factor 
curves are determined from the theoretical values 
modified by the field test results. These latter A 
factor curves are suital/le for tossing rockets with the 
bomb director, Mark 1 Model 2, AN/ASG-IOA. 


7.4.2 Theoretical Yalnes for A Factor 

A derivation of the formula for the pull-up time 
for rocket tossing gives a theoretical expression for 
the A factor [equation (48)] which, with one excep¬ 
tion, is in satisfactory agreement with values 
determined . experimentally by field tests.^ The 
derivation is based upon data on the gravity mil 
drops of rocket trajectories given in CIT publica¬ 
tions 216 , 21/.218 describe the motion of the rocket 
after firing. These data on mil drops are used in the 
form of empirical ecpiations which fit the data over 
usable ranges of the variables within about two mils 
(see Section 7.1). The theoretical expression for the 
A factor is given Iw equation (31a), Chapter 2: 

„e -y/o, (48) 

g 

where a and b are constants for each rocket type, V 
is the true airspeed of the airplane (feet/second)^ 
g is the acceleration due to gravity, and e the base 
of natural logarithms. The values of a and h for five 
Navy rockets now in use are given in reference 177. 

Plots of theoretical values of A as given by equa¬ 
tion (48) against true airspeed in knots are given in 
Figure 11 for five Navy rockets now in use. 

The values for the A factor in Figure 11 are for 
firing from a zero-length launcher with rocket toss¬ 
ing equipment which has provisions for setting in 
the propellant temperature (and lanjmrd length in 
the case of lanyard firing of the 11.75-inch AR). 
The values for the A factor are good onh" when the 
gunsight is aligned along the flight line of the aircraft. 

The data on mil drops of the rocket trajectories 
were obtainable only to 2,000 yards slant range for 
all of the rockets treated, except the 3.5-inch AR,. 
5.0-inch HVAR, and 11.75-inch AR. Thus the cal- 


^The experimentally determined A factor for the 11.75- 
inch AR is considerably higher than the theoretical value. 
As yet no reason for this discrepancy has been found. 

















EVALUATION OF THE A FACTOR 


155 


culated A factors given are partially dependent on 
extrapolations at ranges beyond 2,000 yards for the 
rockets not excepted in the previous sentence. 



Figure 11. A factor (A 2 ) versus V for different types of 
rockets, for firing from zero-length launcher. 


Effect of Plane Velocity 
on A Factor 

As may be seen from Figure 11, the A factor 
increases nearly linearly with true airspeed of the 
plane. Field tests have shown that if the A factor 
for a particular plane speed is set into the equipment 
the shift in MPI obtained when a different plane 
speed is used is small — about 1 mil per 10 knots 
deviation from the set value (see Sections 2.2.10 and 
5.3). Thus satisfactory results should be obtained 
at airspeeds within 20 or even 30 knots of the set 
value. The reason for the small MPI shift with 
velocity with the toss sight is that the change in 
attack angle of an airplane in a dive causes the ]\IPI 


to go long as the airspeed increases, whereas the 
error due to having the A factor set too low at the 
higher speeds causes the rounds to land short. As a 
result the two effects partially cancel, and the error 
due to airspeed changes from the preset value is 
reduced. 


A Factor as Based on Ratio 
of Plane to Rocket Speed 


When the trajectory drop is evaluated by assum¬ 
ing that the rocket has a constant velocity after 
firing (see Section 2.2.2), the A factor is given by Ai. 
V 


Ai — 


F +Fb 


(49) 


where F is the plane velocity and (F + Vr) is essen¬ 
tially an average velocity of the rocket over the inter¬ 
val between the plane and target. The expression in 
equation (49) requires a known value for (F + Fj?) 
for evaluation. It will be shown in the following 


1800 

1700 

1600 

ISOO 

1400 

1300 


1600 - 
1500 - 
1400 — 
1300 — 
1200 - 


PLANE VELOCITY =400 KNOTS 



1000 2000 3000 4000 


PLANE VELOCITY *300 KNOTS 








1000 


2000 


3000 4000 


1500 

1400 

1300 

1200 

1100 


PLANE VEL0CITY=200 KNOTS 



1000 2000 3000 4000 

SLANT RANGE (YARDS)- 


Figure 12. Average rocket velocity versus slant range 
at different plane velocities, as obtained from tabulated 
flight times for 5.0-inch HVAR (encircled points). Hori¬ 
zontal lines marked V + Vr represent theoretical values. 


paragraphs that if the quantity {V + Vr) is obtained 
from the slant range divided by the rocket flight 
time given in CIT publications, 216 . 217,218 
value of AI computed by equation (49) Avill give 
values comparable with those given by equation (48) 
and plotted in Figure 11. This will be shown by 
equating the two expressions (Ai and A 2 ) for the 
















156 


MATHEMATICAL THEORA^ OF ROCKET TOSSING 


A factor and solving for (T" + Vr). Then the values 
of (T + obtained will be compared with the 
total rocket velocity obtained from the flight times 
at various ranges. Equating Ai and A 2 and solving 
for (E + Ffl) we have 

- V/2h 

f- e ■ ( 50 ) 

2 a 

In Figure 12 are shown plots of the average rocket 
velocity against slant range for the 5.0-inch HVAR. 
(Similar graphs for the 3.5-inch AR are given in 
Appendix D of reference 188. No velocity data are 
available for the 2.25-inch AR (fast)). The average 
rocket velocity is obtained from the flight time of the 
rocket as a function of range at plane speeds of 
200, 300, and 400 knots. Also given on the graphs is 
(T^ -b Vr) as calculated from equation (50). Thus 
it is seen that if (T^ + T”/?) is determined from an 
average value of the rocket flight time divided into 
the slant range, the values of Ai given by the square 
of the ratio of plane velocity to rocket velocity are 
in substantial agreement with the values of A 2 given 
in Figure 11 from equation (48). 


^ ^ ^ Comparison of Experimental 
and Theoretical Az Values 

Table 4 gives values of A determined from field 
tests on rocket tossing, and the theoretical value of 
A 2 from equation (48) for the particular plane speed 
used. 


Table 4 


Rocket 

Plane 

Average 

TAS 

(knots) 

Theoretical 
.42 value 
from equa¬ 
tion (48) 

Experimental 

A value adjust¬ 
ed to give no¬ 
wind MPI 
on target .4 —.42 

3.5-in. AR 

TBM-IC 

295 

0.187 

0.192 

0.005 

3.5-in. AR 

TBM-IC 

255 

0.152 

0.168 

0.016 

3.5-in. AR 

F4U-1D 

345 

0.232 

0.226* 

- 0.006 

3.5-in. AR 

P-47D 

320 

0.210 

0.220 

0.010 

5.0-in. HV.AR 

F6F-5 

360 

0.146 

0.158 

0.012 

5.0-in. HVAR 

F6F-5 

370 

0.152 

0.158 

0.006 

5.0-in. HVAR 

F4U-1D 

340 

0.135 

0.143 

0.008 

5.0-in. HVAR 

SB2C-4 

355 

0.142 

0.158 

0.016 

5.0-in. HVAR 

F4U-1D 

350 

0.140 

0.130* 

-0.010 

2.25-in. AR 

F4U-1D 

340 

0.221 

0.260* 

0.039 

(fast) 






5.0-in. AR 

F4U-1D 

340 

0.301 

0.307* 

0.006 

5.0-in. AR 

F4U-1D 

345 

0.306 

0.300* 

— 0.006 

11.75-in. AR 

F4U-4 

355 

0.210 

0.305* 

0.095 

11.75-in. AR 

F6F-5 

345 

0.202 

0.290* 

0.088 


* With temperature compensation and a 7.5-megohm leakage resistor. 


It will be noted from Table 4 that the theoretical 
A 2 was slightly lower than the experimental value 
when the equiinnent did not contain the temperature 
compensation feature. This is as expected, since a 
somewhat larger A factor was required to compensate 
for the increased mil drop due to the somewhat low 
temperatures of propellant used in the tests. For 
ecpiipment containing the temperature compensation 
feature, the theoretical A 2 is more nearly the exper¬ 
imental A, except for the 2.25-inch AR (fast) and 
the 11.75-inch AR. In view of the data limitation in 



Figure 13. A factor versus 4' for different types of 
rockets from theoretical curves modified by field test 
results. 


obtaining the theoretical A 2 for the 2.25-inch AR 
(fast), data available only to 2,000 yards, it is not 
surprising that a larger A factor is necessary in 
practice. As previously stated, no reason has yet 
been found for the large disagreement between the 
theoretical and experimental A values for the 11.75- 
inch AR. 

Plots of the A factor as determined from equation 










COMPENSATION FOR TEMPERATURE AND LANYARD 


157 


(48) and modified by field test results to give an 
on-target no-wind i\IPI under average conditions, 
are given in Figure 13 for five Navy rockets now in 
use. As noted by comparing Figures 11 and 13, 
there was a small modification for the 2.25-inch AR 
(fast) and the 5.0-inch HVAR; and a rather large 
modification for the 11.75-inch AR.® The A values 
for the 11.75-inch AR in Figure 11 are slightly 
higher than those used in determining the rocket 
calibration settings given in reference 18G. 

Conclusions 

The A factors plotted in Figure 13 are sufficiently 
accurate to be used to predict results, and to set up 
the rocket tossing equipment, bomb director Mark 1 
Model 2, AN/ASG-lOA in a plane. It should be 
noted, however, that the values of A should be 
increased by about 0.01 at median temperatures if 
old style experimental equipment without tempera¬ 
ture compensation is used. 

The simplified picture of rocket tossing in which 
the A factor is given by the square of the ratio of 
plane velocitj'" to rocket velocity is essentially 
correct. Also, if the average rocket velocity is 
obtained from the value of the slant range divided 
by the flight time recpiired for the rocket to get to 
the target, and A is computed from it, the value 
obtained is essentially in agreement with field results. 

7 5 COMPENSATION FOR PROPELLANT 
TEMPERATURE AND LANYARD 
LAUNCHING^ 

^ ^ * Introduction 

It is necessary to take account of propellant 


temperatures is due to the fact that gravity has a 
longer time to act during the longer burning times 
which arc obtained. In the launching of large rockets, 
a lanyard is used to fire the round a short time after 
release in order to minimize the damage to the ]>lane 
from the rocket blast. In order to toss rounds when 
lanj^ard launching is used, as with the 11.75-inch 
AR, it is necessary to add to the pull-up angle an 
amount equal to the mil drop of the trajectory during 
the delay period between release and firing of the 
round. Since these two effects are similar in that an 
amount independent of slant range is to be added to 
the pull-up angle to compensate for a gravity mil 
drop occurring before the end of burning, they are 
treated together. 

Section 7.5 will describe the function the com¬ 
puter is required to perform to compensate for tem¬ 
perature and to allow lanyard launching. The neces¬ 
sary modifications to the computer circuit will then 
be described. The theoretical calibration formulas 
for the temperature and lanyard compensation dial 
are given, and a section is devoted to the experimental 
data obtained recently as compared with the the¬ 
oretical calibration. 


7.5.2 Equation to be Solved 

by Computer 

Equation (19) has been obtained as a formula for 
the pull-up time for rockets. The present rocket 
tossing equipment (Mark 1 Model 2) has a second 
capacitor charging rate which is proportional to ^ 
for K < 1.3, and to (K + — K)/A for /v > 1.3; 

that is, during the interval in which K < 1.3, the 
charging rate is much too small, while for K > 1.3, 
it is too large in the ratio 


_ K + V/v^ - K _ 

K — cos a -f F{a)A 2 {V) 4- V(A' — cos a) [K — cos a + F(q:)A 2 (F)] 


temperature in rocket tossing, as the trajectory drop 
of a rocket is considerably increased at low pro¬ 
pellant temiieratures. The increased drop at lower 

s See footnote f, Section 7.4.2. 

h Section 7.5 was prepared by I. II. Swift, formerly of the 
State University of Iowa, now at Naval Ordnance Test 
Station, Inyokern, California. 


This ratio is greater than unity for dive angles less 
than about 70 degrees, the exact angle depending 
upon A 2 and K. Thus, two errors of opposite sign 
are introduced in the pull-up time, the net error 
depending upon the relative durations of the condi¬ 
tions K <1.3 and K > 1.3. For the remainder 
of this section, it will, therefore, be assumed that the 
















158 


MATHEMATICAL THEORY OF ROCKET TOSSING 


equation to be solved by the computer is 


+ 27’i 


- Am 


Tp = 4'' 


K + ^lK^ - K 


(51) 

this being obtained l^y replacing F{a) in the numer¬ 
ator of equation (19) by \J/ for boml)s (see Figures 2 
and 3, Chapter 2), and replacing the denominator 


by K -f VA '2 _ Ay 


’ ^ INIethod of Compensating 
for Temperature and Lanyard Drop 


Equation (53) may be put into the equivalent form 
Ay = yo + - 1] = 150 + - 1] (53'> 


where 


and 


r 


^ Td (^ 
10 \ ArP 



^ ^ c hjr) 

10 Ag 

Ecjuation (53') may l>e approximated b}^ the 
equation 

Ay = 179(?* + s)\p, (54) 

for the range of values of r, s, and yp occurring in 
rocket tossing. This is shown in Table 5. 


The method of introducing the lanyard and 
temperature term into the equation for Tp solved 
by the computer, and the derivations of the theoret¬ 
ical calibration formulas, will be shown in Section 

7.5.3. 

1. Method. If the capacitor added to the bomb 
computer circuit to introduce the A factor is charged 
negatively with respect to ground by Ay volts at the 
initiation of pull-up, the Tp given by the computer is^®^ 

A^pr, -f 20A ln( 1 + - 

rj. _ ^ ^0 

K + VA2 - K 

where \p is the \p function for bombs, t’o is the charging 
voltage for the condensers, and In is the natural 
logarithm. According to equation (52), a term is 
added to Tp which is inversely related to K and 
directl}'' proportional to A. 

Since the pull-up angle a.ssociated with a change of 
amount ATp in Tp is (K — cosa)gA7\/V, the effect 
of the second term in the right-hand member of 
equation (52) is to increase the pull-up angle by an 
amount which is independent of range, and inversely 
proportional to airplane velocity. On the other hand, 
the angiUar trajectory drops associated with rocket 
propellant temperature and lanyard firing delay 
period are seen from equation (33), Chapter 2, also 
to be independent of range and inversely propor¬ 
tional to velocity. Thus, the desired type of correc¬ 
tion is provided by equation (52). 

In order for equations (51) and (52) to be equiva¬ 
lent, the relation (53) must hold. 

(53) 



Table 5 


(?• + s) 

179 (r -f s) 

150[e ('• + »)';' - 1] 

0.1 

17.9 

15.78 

0.2 

35.8 

33.21 

0.3 

53.7 

52.48 

0.4 

71.6 

73.77 

0.5 

89.5 

97.31 


2. Determination of r. The quantity r is zero for 
small rounds fired from zero-length launchers. Eor 
the 11.75-inch AR, which is fired with a lanyard, the 
A factor is approximately 0.30. At a dive angle of 
35 degrees, the quantity cos a/\p equals 1.18 for the 
\p corresponding to Tc/V = 0.03. This results in the 
formula 

r = 0.29 Td. (55) 

The value for Td to be used in equation (55) can 
be obtained from Table G, which is based on equa¬ 
tion (16). 


Table 6 

1 

Kd = 3 

Kd = 4 

77" 

0.365 

0.317 

36" 

0.250 

0.217 


3. Determination of s. Considerable data have 
been taken at Inyokern^^® with the 5.0-inch HVAR 
with tossing equipment which did not include 
temperature compensation. These tests were made 
at propellant temperatures from 50 to 70 F, and 
they show’ no significant shift (less than 2 mils) in 



















COMPENSATION FOR TEMPERATURE AND LANYARD 


159 


MPI with variation in range out to 4,000 yards. 
Since the equipment without temperature com¬ 
pensation does not take account of the term of 
equation (51) which is independent of range, it is 
concluded either that the CIT theoretical mil 
drops^^^’’"^^'^^^ are in error, in that the constant term 
should be zero at field temperatures, or that some 
unknown factor adds a constant amount to all 
pull-up angles. Furthermore, as will be shown in a 
following paragraph, the field measurements on the 
shift in IMPI with temperature give shifts con¬ 
siderably larger than those given in CIT tables. 
The CIT values have mot been experimentally 
checked by firing rounds of different temperatures 
from airplanes. It should be noted that both of these 
discrepancies are the result of comparing deductions 
based on tossing results with theoretical calcula¬ 
tions made by CIT on the trajectory of a rocket 
during the burning period, which is the most uncer¬ 
tain part of the trajectory. The toss results are in 
agreement with CIT calculations of the trajectory 
after burning. 

The function h{T) will now be altered so that it 
will vanish at T = 100 F; thus permitting com¬ 
pensation for temperature to be made for any 
temperature lower than 100 F. This change w’ill 
require the use of a smaller A factor, and the MPI 
will be a few' mils short at long ranges. This will be 
taken care of by mserting leakage resistance in the 
second charging circuit. The new' functions are 
denoted by H{T), and are given in Table 7. 


Table 7 


Rocket 


2.25-in. AR (fast) 
3.5-in. AR 
5.0-in. AR 
5.0-in. HVAR 
11.75-in. AR 


H{T) 


7'2_240r + 14,000 
— 350 T + 25,000 
7'2 — 350T + 25,000 
r- — 20 iT 4- 16,400 
T2 — 240T + 14,000 


The fact that the theoretical CIT mil drojis do 
not agree w'ith experimental firing tests as regards 
the magnitude of the MPI shift w'ith temperature 
will now’ be considered. For example, the CIT 
tables give for the 5.0-inch HVAR a shift of 8.5 mils 
for a temperature change from 0 F to 100 F for flight 
conditions of 35-degree dive, TAS of 350 knots, and 
2,500 yards slant range; whereas experimental data 


at Inyokern wdth both an F6F-5 and an F4U-1D give 
a shift of about 15 mils under the same condi- 
tions.^^®'One way to take care of this discrepancy 
is to use the ratio 15/8.5 = 1.76 as a factor to be 
multiplied into the values of c given in Table 2. 
Other later data gave, how’ever, a slightly smaller 
MPI shift with temperature, indicating that a factor 
of about 1.5 should be used. These later tests con¬ 
sisted of use of the temperature compensation 
control to keep the iMPI on target for various pro¬ 
pellant temperatures, and therefore are more perti¬ 
nent measurements. Hence, the value 1.5 will be 
used for the factor to be multiplied into c. Since 
field data are available onh^ on temperature effect 
with the 5.0-inch HVAR, the same factor will be used 
for all rockets. This results in values for C = 1.5c 
given in Table 8. 


Table 8 


Rocket 

C = 1.5c 

2.25-in. AR (fast) 

6.3 X 10-“ 

3.5-in. AR 

4.95 X 10-“ 

5.0-in. AR 

4.95 X 10-“ 

5.0-in. HVAR 

5.6 X 10-“ 

11.75-in. AR 

6.3 X 10-“ 


The value of s is now’ given by 


CH{T) 
lOAg ' 


(56) 


In computing s for a given case, the value of A may 
be taken from Figure 13. It should be noted that the 
value of s given by equation (56) is not the same as 
the earlier s. 


7.5.4 Ingtriimentation and Calibration 

It is seen from equation (54) that the voltage Av, 
to w'hich the rocket calibration capacitor must be 
charged negatively, is proportional to The neces¬ 
sary initial voltage Ay can be obtained to a sufficient 
degree of approximation from the output voltage of 
the gyro, as this voltage is approximately propor¬ 
tional to i/'. The gyro voltage is positive with respect 
to ground but, by a suitable circuit arrangement, the 
rocket condenser is charged positively betw’een 
arming and pull-up, and then reversed in the circuit 
at the initiation of pull-up. Thus, the capacitor is 













160 


MATHEMATICAL THEORY OF ROCKET TOSSING 


negatively charged to a voltage proportional to xp. 
The proportionality constant is determined hy the 
setting of a potentiometer that applies a portion of 
the gyro output voltage to the capacitor. The setting 
of this potentiometer (the temperature and lanyard 
control) is determined by the values of r and s. 
The circuit of the present production model (Mag- 
navox) of the Alark 1 Model 2 bomb rocket tossing 
equipment includes the features just described, and 



Figure 14. Temperature compensation voltage Av 
versus temperature T for different velocities V for 5.0- 
inch HVAR. 


IS shown in Figure 9 of Chapter 3. The circuit for 
the Mark 1 Alodel 0 is identical in performance 
with the Magnavox circuit (Mark 1 Alodel 2). 

If the gyro voltage is v/, then 

Av = kvf. (57) 

Comparison of this equation wdth equation (54) 
shows that k is given by 

k = 179 (r + s)-. 


But at a mean dive angle of 35 degrees, the value of 
150is about 0.9. Hence, 

k = -(r + s) = 1.0/(r + s). 

150 

The temperature-lanyard control dial is marked 
with numbers which designate the voltage Ai’o when 
the dive angle is zero. Since Vf = 150 when the dive 
angle is zero, it follows from equation (57) that 

Aco = A- X 150 = lGl(r 4- s) = 477^ -f 161s. (58) 

In ecpiation (58), the delay time may be taken 
from Table 6 or computed from formula (16), and 
the value of s is from (56). 

For example, for the 11.75-inch AR fired using a 
lanyard of effective length 77 inches, the value of 
I'd may be taken as 0.3 second. If a propellant 
temperature of 60 F is assumed, and a velocity of 
300 knots (corresponding to A = 0.24), the value of 
s from (56) is 0.026. Hence, 

Avo = 47 X 0.3 + 161 X 0.026 = 18.3. 

Figures 14 and 15 .show the temperature compensa- 



Figure 15. Temperature compensation voltage Av 
versus temperature T for different velocities V for 11.75- 
in cli AR. 


tioii voltages for the 5.0-inch HVAR and 11.75-inch 
AR, as obtained from equation (58). (For other 
types of rockets, see Appendix E of reference 188.) 

















COMPENSATION FOR TEMPERATURE AND LANYARD 


161 


® ® Comparison of Experimental 
and Theoretical Values 

Equipment containing the propellant temperature 
compensation control was used to fire 5.0-incli 
HVAR’s at Inyokern, all at the same temperature, 
in order to determine the shift in The follow¬ 

ing results were obtained. 


Number of 

Temp, control 

MPI 

rockets 

(volts) 

(mils) 

22 

0 

- 2.9 

6* 

8 

8.4 

6* 

30 

9.0 

16 

30 

14.0 


* Only one pair from one direction, together with a high wind, makes 
these data of small value. This series of tests showed a shift in the proper 
direction. 


In a second series of tests,rockets were heated 
or cooled to the extreme allowable temperatures, 
then compensation w'as made on the temperature 
controls according to the theory, all other factors 


remaining 

obtained. 

the same. The 

following results 

were 

Number of 

Prop. temp. 

Temp, control 

MPI 

rockets 

(degrees F) 

(volts) 

(mils) 

9 

102 

0 

-5.1 

14 

63 

8 

3.1 

15 

11 

30 

-2.1 


The MPI is slightly short at both extremes, but 
the small number of rockets used makes the signifi¬ 
cance of this small error questionable. 




Chapter 8 

DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


8 1 ADVANTAGES AND LIIVIITATIONS 
OF THE MARK 1 BOMB DIRECTORS 

A s POINTED OUT in the preceding chapters, the 
Mark 1 bomb director affords a definite im¬ 
provement in the accuracy of dive-bomliing opera¬ 
tions. Quantitative measure of the advantage of 
the toss method varied with the Service liranch 
conducting the evaluation, but all indicated some 
gain. The greatest advantage was indicated by 
Navy tests, probably on the basis of more extensive 
evaluation. This numerical advantage, as indicated 
in Section 5.1.1, was about two and one half times. 
A further advantage, difficult to express in quanti¬ 
tative terms, lay in the simplicity of the toss methods 
in actual use. The automatic properties of the equip¬ 
ment required only limited concentration from the 
pilot, and it was felt that under the stress of battle 
conditions this vould show as a very decided ad¬ 
vantage. The operational use of Model 0 established 
the latter factor if one accepts as pertinent the 
enthusiastic reception of the equipment by the 
pilots who used it in combat. (See Section 5.1.2, 
and reference 2G9.) 

It was evident that there were a number of ways 
in which the Mark 1 equipments could be improved, 
and considerable effort was made to develop instru¬ 
mentation of still greater accuracy and reliability. 
Probably the greatest difficulties in the production 
and maintenance of Mark 1 directors were encoun¬ 
tered in the altimeter and gyro units and in the 
potentiometer which measured acceleration. In the 
case of the altimeter and gyro most of the difficulty 
was undoubtedly due to the fact that these were 
standard items modified to fit into the computer 
equipment and not specifically developed for the 
purpose. A common factor and limitation in all these 
items was the sliding or moving contact. Contact 
trouble could and did arise from a variety of sources 
such as vibration, dirt, jiressure adjustment, and 
wear. A completely new computer circuit was de¬ 
signed, using new" methods for indicating altitude, 
dive angle, and acceleration, and in which the sliding 
or variable contacts were either eliminated or greatly 
modified. This equipment, tentatively designated 
bomb director, Mark 3, Model 0, AN/ASG-lOB, is 


described and discussed in Section 8.2. The Mark 3 
director had not been evaluated in field tests at the 
end of the w'ar. 

Evaluations of the IMark 1 director show'ed that 
even though the equipment would inherently give 
excellent accuracy, this accuracy in Service use could 
be appreciably reduced through inadequate w’ind 
correction. Hence it became imperative to provide a 
method for estimating and making the proper 
trajectory correction for wind, if the full value of the 
instrument was to be utilized. The methods em¬ 
ployed for this purpose w’ith Mark 1 directors have 
been described in Chapters 2 and 6. These methods 
w'ere, however, essentially improvements and ap¬ 
pendages to the bomb director. In the Mark 3 
director, the accelerometer to measure dive angle 
provides some correction for range wdnd error (see 
Section 8.2.4). The use of a lead-computing sight in 
conjunction with the director w'ould provide a still 
greater correction. The principle of the use of this 
is described in Section 8.3. 

The i/' function which represents the correction 
applied to the computing process for dive angle and 
other factors, w'as the least accurate intelligence fed 
to the computer. Although \}/ can be formulated 
exactly (as shoAVn in Chapter 6) instrumentation of 
the exact solution w'as not practicable. The i/'i func¬ 
tion used in the Model 1 unit Avas an improvement 
of the \po function, but Avas still subject to a number 
of limitations as AA'as shoAvn in Chapter G. More 
recently another formulation of the function, 
designated as \pr, was devised, AA'hich offers even 
greater advantages. The \pr function is formulated 
and discussed in Section 8.4. 

8-2 THE MARK 3 MODEL 0 

BOMB DIRECTORS 

Altimeter Cireuit 

In the Mark 3 Model 0 (AN/ASG-lOB) bomb 
director,*® the time to target is measured by the use 
of tAA'o pressure capsules coupled to a potential 

a Section 8.2 was written by William B. IMcLean, formerly 
of the Ordnance Development Division of the National 
Bureau of Standards, but uoav at the Naval Ordnance Test 
Station, Inyokern, California. 


1G2 



THE MARK 3 MODEL 0 BOMB DIRECTOR 


1G3 


divider, /?2G (Figure 1), in such a way as to provide a 
voltage which is proportional to the pressure altitude. 
This unit is approximately the size of a standard 
altimeter and is pictured in Figure 2. It has been 



Figure 1. Sctiematic diagram of altimeter control 
circuit for Mark 3 bomb director. 


tested in the Aeronautical Instruments section of the 
National Bureau of Standards and found to perform 
satisfactorily.'^^ The barometric unit is used in con¬ 
junction with the electronic circuit shown in Figure 1. 
The unit is connected across a 300-volt source of 
d-c power. The voltage at the sliding contact is 
applied to the grid of a tube, Tj, used as a cathode 
follower. The high input impedance of this circuit 
insures that the effect of any contact resistance will 
be negligible. A capacitor, (715, connected to the grid 
of the cathode follow'er maintains the grid at a con¬ 
stant potential in the event that the sliding contact 
momentarily breaks contact with the potential 
divider. 

The adjustment of the instrument for changes in 
pressure and target altitude is accomplished liy 
means of the potential divider, A^37, and the variable 
resistances, A38 and A39. The scale on resistor A37 
is calil^rated in feet of altitude and can be set at 
altitudes from —500 feet to +7,500 feet. Ro.sist- 
ances A38 and A39 are ganged together so that A38 
increases as A39 decreases. They permit the altitude 
scale to be set to compensate for varying atmospheric 
pressures. The dial controlling them is calibrated in 
inches of mercury. 

To adjust the altimeter liefore starting a bombing 
mission, the altitude dial is set to the geographical 
altitude of the airplane. The test switch is closed to 


connect the meter between the cathodes of tubes 
and The pressure compensating resistors, 
A38 and A39, are adjusted until the meter reads zero 
current. The dial will then indicate sea level pressure. 
The altitude dial is reset to the altitude of the target 
and under these conditions the voltage between the 
two cathodes w'ill be zero at the target altitude and 
the voltage difference lietween them will be propor¬ 
tional to the altitude above the target. 



Figure 2. Altimeter control unit for Mark 3 Model 0 
bomb director. Note the potentiometer and sliding 
contact at the right. 

The capacitor, ('A4, is so arranged that the opera¬ 
tion of relay contacts lA and \B will cause the grid 
of the thyratron to become negative by a voltage 
corresponding to one-sixth of the altitude above the 
target. As the altitude decreases, the contact on the 
altitude potential divider moves toward the positive 
end and the thjuatron grid voltage rises. The thyra¬ 
tron grid reaches the zero firing potential when the 
altitude has decreased to five-sixths its original 
value. The interval between the time at w'hich 
contacts L4 and \B operate and the time at which 





























164 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


the thyratron fires is the time reciuirccl for the plane 
to travel 1/5 of the distance to the target. 

The altimeter described above has the following 
advantages over the contacting altimeter previously 
used: 

1. The output is continuous so that the timing 
operation is started as soon as the bomb release 
switch is closed. This ^\ill re.sult in shorter timing 
runs. 

2. Its mechanical construction is materially simpler 
than that of the standard commercial altimeters 
which have hitherto been modified to produce the 
Mark 1 altimeter unit, and the force acting at the 
electrical contact can be much greater. 

3. The adjustment of the altimeter for target 
altitude and pressure is accomplished electrically so 



Figure 3. Scliematic diagram of photoelectric accel¬ 
erometer control circuit giving negative output voltage. 



Figure 4. Photoelectric accelerometer unit. At the bottom right is jihotocell on its mount; at bottom left, condensing 
lens. At top left is case for 2b^-inch milliammeter. At toj) center is shown meter movement; note, at end of pointer, flag 
partly covering aperture. At toj) right is back view of assembled unit, minus photocell and its mount. 























THE MARK 3 MODEL 0 BOMB DIRECTOR 


165 


that the controls may be located remote from the 
altimeter unit. This will result in a reduction of the 
amount of equipment which must be made accessible 
to the pilot. 

8 . 2.2 Photoelectric Accelerometer 

The photoelectric accelerometer unit consists of a 
33/^-inch panel milliammeter, the movement of which 
is unbalanced by the addition of a weight to the end 
of the pointer. The weight serves also as a shutter to 
cover a slot in the instrument face. A photocell 
(T'21) is mounted behind the slot and is connected 
in a circuit of the type illustrated in Figure 3. The 
instrument is connected with such a polarity that an 
increasing current tends to move the hand in such a 
way as to decrease the light falling on the photocell, 
pictured in Figure 4. It is clear that the light falling 
on the photocell will adjust itself until the torque 
due to the current through the instrument coil just 
balances the torque due to the unbalance of the 
movement. If the acceleration normal to the plane 
containing the center of gravity of the movement 
and the two pivot points is changed, the current will 
immediately readjust itself until a balance is re¬ 
stored. The current through the instrument is 
therefore always proportional to the acceleration 
acting normal to the pointer. As long as there is 
sufficient amplification in the photocell circuit to 
maintain a balance, the circuit characteristics do not 
affect the output current. The output is also inde¬ 
pendent of variations in photocell sensitivity and 
light intensity. 

Damping and Response 

An electrical damping force is provided by the 
capacitor Cl. If the pointer changes its position, the 
photocell circuit and capacitor immediately cause a 
high current to flow in the coil which opposes the 
motion. This transient current dies out as the motion 
ceases and is analogous to viscous damping in a 
purely mechanical system. It has a magnitude which 
depends on the angular velocity of the coil. 

If the pointer bends, the motion of the coil is not 
in phase with the motion of the shutter controlling 
the photocell current. In this case the damping force 
described above may become a driving force and the 
moving system may oscillate. The oscillation is of 
such frequency that the pointer has a node about 


one-third the distance from the free end to the pivot, 
Such oscillations, which have a frequency of 250 
cycles per second, can be prevented by decreasing the 
gain of the system for high frequencies and by increas¬ 
ing the stiffness of the pointer. 

Capacitor Cll and resistor R16, Figure 3, are 
adjusted for any particular type of instrument 
movement so as to allow as much high frequency 
response as possible without running into danger of 
oscillation due to bending of the pointer. 



Figure 5. Schematic diagram of photoelectric accel¬ 
erometer control circuit giving positive output voltage. 

Figure 5 shows a similar circuit arrangement in 
w'hich the instrument coil is in the cathode circuit 
of the control tube in place of the plate circuit. Both 
arrangements are used in the Mark 3 computer. 
The circuit of Figure 3 is adaptable to securing a 
negative output voltage with respect to ground and 
that of Figure 5 is more easily used to secure a 
positive voltage with respect to ground. 

It should be noticed in both Figures 3 and 5 that if 
the output voltage is taken from the tube side of the 
control instrument coil, it will not be affected by 
changes in output load. If it is taken from the 
opposite side of the coil, it will be affected by changes 
in output load but will not be affected by changes in 
resistance of the instrument coil. 

Centrifuge Tests 

An accelerometer unit of the type described above 
was checked for linearity and stability by mounting 
it on the arm of a centrifuge. The speed of the 






















166 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


centrifuge was adjusted until the current through 
the instrument was a certain fixed value as deter¬ 
mined by means of a standard 1-ohm resistor and a 
potentiometer. Then revolutions of the centrifuge 
were timed by means of an electric stopclock. 
Readings were the same to within the estimated 
accuracy of setting the potentiometer. The voltage 
output versus acceleration showed a high degree of 
linearity.^® 


Nonlinear Output 


It is desired that the output voltage of the 
accelerometer be a nonlinear function of the accel¬ 
eration. Since the current through the instrument 
is exactly a linear function of the acceleration it is 
necessary to make the resistance, across w'hich the 



Figure 6. Graph of desired acceleration function; 

(yPi (arc cos A', 3, 0.028) (0 < A < 1) 

Dashed lines represent proposed straight line fit: 

fFatA) = 1.1207A - 0.19224 (0 < A' < 1) 

F(A) ^ \ Fi{K) = 2.6115A - 1.6115 (1 < A < 1.5) 
Fi(A) = 2.0069A - 0.7046 (A > 1.5) 


consist of a series of straight lines. The transition 
from one line to another occurs wdienever the current 
through one of the branches containing a diode 
changes its direction. By properly selecting resistor 
values, it is possible to fit the desired curve with a 
series of straight lines.The desired function of 
acceleration is shown in Figure 6. The dotted lines 
show the proposed straight line fit. 

It is necessary to adjust the current through the 
meter movement under a standard acceleration to 
an exact value in order to obtain the proper curves 
by the above methotl. This is done by the use of a 
variable magnetic .shunt which can be adjusted 
w'hile the meter is operating under an acceleration 
of Ig. 


8.2.3 Dive Angle Indication 

In bomb tossing, it is necessary to determine the 
component of gravity acting normal to the line of 
flight since this is one of the factors that will deter¬ 
mine how long the bomb will stay above the line of 



Figure 7. i/' function for Mark 3 director, as function 
of cos a, determined for A = 3 and T^/V = 0.028 (solid 
curves); dashed lines give the straight line fit: 


iAi(«,3,0.028) 


0.9906 cos a: —0.115 
1.676 cos a — 0.676 


(0 < cos a < 0.82) 
(0.82 < cos a < 1) 


output voltage is developed, vary with the accelera¬ 
tion in order to obtain a nonlinear output voltage. 
By means of the diodes show'n in Figures 3 and 5 it 
is possible to obtain voltage-current curves which wall 


flight. The Mark 3 director uses the sensitive accel¬ 
erometer described above to measure this component 
of acceleration during the timing run. The current 
through the accelerometer during the timing run is 































THE IMARK 3 MODEL 0 BOMB DIRECTOR 


167 


proportional to cos a. A capacitor is charged in such 
a way that its voltage is proportional to: 

0 

\p {a)dt. 

Tcl5 

Figure 7 shows a graph of \l/(a), as a fimction of 
cos a, together with the two straight lines used in 
fitting it.“^ 

* Wind Correction 

The use of an accelerometer to measure dive angle 
provides some correction for the range-wind error as 
described in Section 6.6.9.*^ This is due to the fact 
that in tracking a target with a head or tail wind the 
plane will fly a curved course. The curvature of the 
path is such that it increases the reading of the 
accelerometer for a head wind, and thus increases the 
value of the acceleration integral set into the com¬ 
puter during the timing run. A longer toss results, 
which decreases the error due to the head wind. The 
converse conditions exist in the case of a tail wind. 

It was suggested that this effect might be increased 
by the use of a lead-computing sight (see Section 
8.3). In using such a sight the airplane must turn 
faster to keep the sight centered on the target. This 
will result in an accelerometer correction to the toss 
which may be sufficiently large to provide full wind 
correction, even though the computing sight does 
not have time to establish the proper lead. 

® Integrating Circuit 

A linear integrating circuit^^ is incorporated in 
the Alark 3 computer. The circuit elements as used 
in the computer are shown in Figure 8. A positive 
voltage, proportional to the function to be inte¬ 
grated, is applied to the input lead. This causes a 
current to flow through resistor R42 to capacitor C5. 
Normally this would produce a rise in potential of 
the input side of this capacitor. Any rise of the grid 
voltage of tube Til, however, causes an amplified 
drop in its plate potential. By means of the cathode 
follower circuit, the potential of the opposite side of 
the capacitor C5 is lowered. The net effect is to 
maintain the grid of tube Til at a very nearly con¬ 
stant potential while the condenser is charging. 
This means that the current flowing to capacitor C5 
is always proportional to the applied voltage. The 


charge accumulated on the capacitor is a measure 
of the integral of the applied voltage during the 
charging period. It is expressed as a drop in poten¬ 
tial of the cathode follower output. If the output is 
connected to a voltage of opposite polarity, the 
reverse operations will take place and the output 
voltage will rise by an amount which is proportional 
to the time integral of the new voltage. 

The fact that the input grid remains at a constant 
potential makes it possible to compute the sum of 
several integrals with this circuit. If several re¬ 
sistors are connected to the input grid and their 
opposite ends connected to voltages proportional 



Figure 8. Schematic diagram of integrating circuit for 
Mark 3 computer. 


to the functions to be integrated, the total current 
flowing to the capacitor will be proportional to the 
algebraic sum of all the functions. The total charge 
on the capacitor will be the sum of the integrals of 
these functions. 

In the Mark 3 computer it is desired to determine 
when the integral of a function of pull-up accelera¬ 
tion is equal to the integral of the dive angle function 
over the timing run, i.e., 

sT yp{a)dt = T"’F{K)dL (1) 

J-Tc/5 Jo 

A positive voltage proportional to 4/{ol) is applied to 
the input of the integrating circuit during the timing 
run. At the second altitude this input lead is con¬ 
nected to a negative voltage proportional to F{K). 
A thyratron releases the bomb when the rise in 
voltage due to the pull-up acceleration is equal to 
the initial drop in voltage. 






















168 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


8.2.6 Provision for Firing Rockets 

It is shown in reference 188 (pages 22-25) that 
the condition for release of rockets, as given l^y 
equation (25) of Chapter 2, can be converted to 

2^ + 5 r Mdt 

A \ g / J-Tc5 

= (2) 

Jo A 

through the following assumptions (see also 

Chapter 2): 

1. That (2 — d) Td is approximate!}^ equal to 2 Td, 
A being a function of plane and rocket velocities; 

2. That 

Fn{K,A) ^ FR{K,Q)+mA, (3) 

reducing to the following relation for bomb 

tossing A = 1: 

Fb{K) ^ Fr{K,Q) + m, (3a) 

and 

3. That yp (a) is, to a sufficiently accurate approxi¬ 
mation, the same function as for bomb tossing. 

The above assumptions are justified in reference 
188 by graphical methods. 

Substituting equation (3) in equation (2), the 
condition for release becomes 


2^ + cKT) 

A \ g 


) + 5 r Hoc. 

/ J- Tc/5 


-f 


)dt 


p Fr{K,()) + mA 


dt 


/o A 

which can be expressed in the form 

I II 

cJi{T) \ 

g 

III IV 

'Tp 1 _ A fTp 

FB{K)dtA—^ / FR{K,0)dt. 

Jo 


2yp{a) ( ^ f 

/ J-T,/5 


-(•' 

j: 


(4) 


A 


(5) 



Figure 9. Graph of bias voltages corresponding to 
different terms of release equation (5). 



Figure 10. Schematic diagram of operation of Mark 3 computer, showing manner in which output voltage components 
are combined (for both bombs and rockets). For terms represented by I, II, III, and IV, see equation (5) in text, except 
that t instead of Tp is upper limit of integration in III and IV. 















































































































































































































































































































































































































♦ t -r'i 


^ tt** ^ "V . 

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■■'■>■>-*iJ.% ■ ' *’t- . r-’ 'i * 

»#<■•*».. I ‘ •<. \. ? . >- • > J 

j:r ■■!■--. v.,:, 

4, i ■• 


WW 

- >* p 

:)yji#oi»3.>5»3A A7r f 

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r.i._pA:.-[i_. 


vr ■■:.;^i. .... ■■r.,.-.^ki 

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4 'A *i^i* n*- ♦” - . 7 f M --, - ---^ , '^i 

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ji' •:■' i Ml ! ! *1 ’ ' 1 • Ir^ ^ 'id 

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-T'«a -ici.. ■; i 1= 

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tmm' ‘r' 3U** •• Is^ ! . *i5*i,' -lU 


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:*'A; 

























HIE MARK 3 MODEL 0 ROMR DIRECTOR 


169 



Figure 12. Photograph of Mark 3 computer. This and control box comprise complete Mark 3 IModel 0 director. 
.Vltimeter is shown at center top of panel; accelerometers are mounted below subpanel. 


Lot the terms in equation (5) be designated by I, II, 
III and IV, respectively. The voltage output corre¬ 
sponding to these terms is shown as a function of 
time in Figure 9. 

The condition for release of bombs is given by 
II — III = 0, and the condition for release of 
rockets is ( - Il-b III) = (I - IV). The block 
diagi-am of Figure 10 shows the manner in which 


these various voltages are obtained and combined. 
It should be noted from Chapter 7 that F}i(K,0) 
^2(K - 1 ). 

Figure 11 is a circuit diagram of the complete 
Mark 3 director. The computer has three output 
circuits, one for releasing bombs or torpedoes and 
two for firing rockets of different types, all on the 
same pull-up. The voltages corresponding to the 






170 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


temperature and lanyard setting are obtained by 
starting the rocket computer circuits at voltages 
other than zero; similarly, the voltage correspond¬ 
ing to the desired stick offset setting for bombs or 
torpedoes is obtained by biasing the bomb computer 
circuit. 

Figure 12 shows a photograph of the Mark 3 
computer which mcludes the altimeter, accelerometer 
and integrating circuits. The only other component 
of the Mark 3 director is the control box in w'hich are 
located all necessary control dials. 

Advantage of 
IMark 3 Bomb Director 

The improvements to be expected from the INIark 3 
bomb director over the Mark 1 bomb director are as 
follows: 

1. The restrictions on maneuvers are removed 
since there is no gyro component. 

2. The altimeter unit has a continuous voltage 
output which will allow the timing run to commence 
at any point. The mechanical construction is simpler 
since no gearing is used. This should result in better 
mechanical performance. 

3. The accelerometer is lighter, more accurate, 
and more easily constructed than the accelerometer 
in the Mark 1 unit. 

4. The iMark 3 director provides for the release of 
a bomb (or torpedo) and two rockets (of different 
types) on the same pull-up. The rocket channels are 
individually adjustable and have sufficient latitude 
to accommodate any type of rocket with or without a 
lanyard release. 

5. A considerable saving in space and weight will 
be possible with this unit. 

6. Partial correction is provided for range wdnds 
as well as for deflection winds. 

USE OF THE 

LEAD-COMPUTING SIGHTS 
8.3.1 Basic Differential Equations 

The. use of a gyroscopic lead-computmg sight 
such as the Navy Mark 18 or Mark 23 


b Section 8.3 was written by Dr. Albert London of the 
National Bureau of Standards, and Dr. L. E. Ward, of Naval 
Oi’dnance Training Station, Inyokern, California. 


(Army K-14) may be characterized by four reference 
lines as shown in Figure 13. In this figure the nota¬ 
tion is as follow's: 



Figure 13. Diagram of reference lines in lead-comput¬ 
ing sight. 

X = angle by which an arbitrarily chosen datum 
line in the airplane leads the sight line at any 
instant. 

7 = angle between sight line and gyro axis at any 
instant. 

cr = angle betw'een sight line and horizontal at 
an}^ instant. 

0a = angle between flight line and datum line at 
any instant; this is the angle of attack. 

Vg = velocity of target, assumed horizontal. 

S = distance from airplane to target at any 
instant. The angles X and y are considered positive 
w'hen the datum and the gyro axis respectively are 
above the sight line; in the figure X is positive and 
7 is negative. 

The sight itself is characterized by two constants; 
(1) the fixed constant a, wdiich determines the rela¬ 
tionship between the motion of the sight line w'ith 
respect to the gyro axis and the motion of the datum 
line with respect to the gyro axis, and (2) the adjust¬ 
able sensitivity constant u, which may be caused to 
vary with range instrumentally and which in the 
case of the LCS as a gunsight is the time-of-flight at 
any instant which the bullet would take to reach the 
target. 

The sight line (sight pip of the LCS) is coupled 
optically to the gyro in such a way that 

7 = nX. (6) 

Usually a is negative, having a value of —0.43 for 
the Mark 23. Hence the sight line w'ill always be 
located betw'een the datum line and the gyro axis, 
as shown in Figure 13. The angle betw'een the datum 
line and the gyro axis is 

X — 7 = (1 — a)X. 






USE OP' THE LEAD-COMPUTING SIGHT 


17.1 


It follows from equation ( 6 ) that 

7 = (X - 7), 

1 — a 

or, the angular displacement of the sight line from 
the gyro axis is always a/(l - a) of the angular 
displacement of the datum line from the gyro axis. 
For the Mark 23, the gyro is displaced 3.33 times as 
much from the datum line as the sight line is from 
the datum line. 

If the effect of angle of attack variations is neg¬ 
lected for the time being, the flight line may be 
considered as coincident with the datum line. Con¬ 
sider the case where the datum line (or flight line), 
the sight line, and the gyro axis are initially coin¬ 
cident, and the target is at rest. If the target starts 
moving, and the pilot starts to track the target, then 
the gyro axis tends to remain fixed in space, and the 
sight line will change by an angle dy. In order to do 
this, the pilot must fly the airplane in such a way 
as to make the flight line change by an angle d{\ — y) 
= —3.33 dy, that is, the airplane will start turning 
at a rate 3.33 times as fast as the sight line turns. 

As the computed lead angle approaches the colli¬ 
sion course lead angle, the rate of turn will decrease 
and will vanish when the correct collision course lead 
is attained. Consequently the differential eciuation 
which the sight must satisfy must be such that the 
required lead angle X* is obtained when X is zero. 
This is accomplished by introducing a precessional 
force on the gyro such that the velocity of precession 
is proportional to the displacement of the gyro axis 
from the datum line and is in such a direction as to 
return the gyro axis to the datum line, that is: 

- y (a- - 7 ) = 6 (X - 7), (”) 

dt 

where h is an instrumental design constant related 
to M and a by the equation 


u{l — a) 

Substituting for h in equation (7) and eliminating 7 
by use of equation ( 6 ) results in the differential 
ecpiation of the sight, namely 

— aw X + X = — Wo-. ( 8 ) 

Figure 14 represents the change in positions of the 
airi)lane and target in time AL By projecting the 
three other sides of the quadrilateral onto S the 
relation 

YM cos X -1- (S 4 - A»S) cos Ao- — F^Af cos a = S (9) 


is obtained, and by projecting the same three sides 
onto a line perpendicidar to S, 

VM sin X = VgM sin o- -f (*8 -|- AS) sin Ao-. (10) 



Figure 14. Diagrammatic representation of changes 
in position of airplane and target in time At. 


From equations (9) and (10), dividing by A^ and 
then making At > 0, the relations (11) are deduced. 

cos X — Ve cos 0 - 4- *8 = 0 
V sin X — Vg sin a = Sa. 

Equations ( 8 ) and ( 11 ) con.stitute three differential 
equations for the three dependent variables X, a, and 
S as functions of t. It is desired to obtain from these 
equations information concerning the rapidity with 
which the lead-computing sight puts the airplane on 
a collision cour.se. 

^ ^ ^ Solution for Collision Course 

In Figure 15 is shown the collision course, point C 
being where collision Would occur if the airplane 
were to fly a straight course in dive angle a. T is the 
time from the instant when X becomes equal to X* 



Figure 15. Diagrammatic representation of lead angle 
for collision course approach. 


to the time of collision. By projecting the lines AC 
and BC onto a line perpendicular to AB the rela¬ 
tion VT sin X* = VeT sin (a 4- X*) is obtained. 








172 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


This reduces to V sin X* = Ve sin (a + X*) or 


tan X* 


Ve sin a 
V — Ve cos a 


( 12 ) 


When solved for the three derivatives, equations 
( 8 ) and ( 11 ) take the form 



au 


V sin X — Ve sin 


y sin X - Ve sin 


(13) 


*S = Ve cos a — V cos X. 

When the quantity dt is eliminated, the pair of 
equations (14) remains. In these equations it is 
convenient to regard S as the independent variable, 
X and (T being dependent varial^les. 

d\ X*S + uV sin X — tiVe sin a 

dS — auS{V cos X — Ve cos a) 

da _ Ve sin a — T' sin X 
dS S{V cos X — Ve cos a) 


The first of equation (14) can be rewritten in a 
form which permits the integration of the important 
terms, the less important terms being treated as 
constants. 

Since X remains close to zero while the airplane is 
still far from the target, and at the same time a 
changes but little, one approximation is to replace 
sin X by X, cos X by unity, and to treat a as though it 
were constant. If this is done, the first of equation 
(14) becomes 

^ 4 - (>S + uV)\ ^ I'e sin (T 

dS auS{V - Ve cos a) aSiV - Ve cos a) 

An integrating factor of this is 

S + mV In S 
gau(V — Ve cos <r) 


and the solution of the differential equation is 

So - S + uV I n SoAS S + M In S y 

X = XoC au (V — V e cos a) -|_ q — au {V — Vecos a) 


rSo Tr • X + mF In ,S 

f _ e ■S^hWr-FT^ dS, (16) 

Js - aS(y - r, cos a) 

where Xo and *So are initial values. 

This solution has been investigated l^y the Applied 
Mathematics Group, NDRC.^”^'^’ 

For the numerical case aSq = 8,100 feet, u = 15 
seconds, I^ = 450 feet/second, 1 4 = 45 feet/second, 
ao = 36.87 (cos 0-0 = 4/5), and the values of a shown 
in Table 1, it is found that when S = 5/6,/So = 6,750 
feet, X has the values shown. 

This table indicates that as a —> 0 from the nega¬ 
tive side, up to 50 per cent of X* may be ol)tained, 
while the term containing the contril:>ution due to Xo 
is minimized. This term can be made zero, of course, 
by uncaging the gju-o at S = So so that Xo = 0. 
Very small values of a are impracticable since the 
rate of turn of the airplane is (1 — a)/a times that 
of the sight line. 


Aiming Procedures 

The INIark 23 sighting head contains a fixed pip 
in the form of a cross, which may be considered as 
fixed rigidly on the datum line, and a movable or 
gyro pip consisting of a dot. In addition there is 
associated with the dot and the movable gyro sight 
field a ring of diamond-shaped points centrally 
located about the dot. Consequently it is possible 
to have various aiming procedures involving aiming 
with the cross, dot, or diamonds in certain specified 
sequences. 

Before describing such procedures, it is advisable 
to state that from a tactical viewpoint, changing the 
aim of the plane during the run requires too much 


Table 1 


a 


- 1 . 


-0.5 


- 0.1 


0.660 Xo + 
0.436 Xo + 
0.016 Xo + 


X calculated from equation (16) 

(0.1629) = 0.660 Xo + ^ (0.1499) 

V V - Ve cos o-o 

(0.2712) = 0.436 Xo + —• (0.2495) 

V V — Ve cos o-Q 

(0.4818) = 0.016 Xo + ^ e sm o-q (q ^^ 33 ^ 

V V — Vg cos o-Q 






























USE OF THE LEAD-COMPUTING SIGHT 


173 


time and increases the number of operations which 
the pilot must perform. In some preliminary field 
tests of these procedures/” it was found that using 
the Mark 23 would reciuire a very skilled pilot, and 
Would deprive the bomb director of one of its prin¬ 
cipal merits, namely, simplicity of operation from the 
pilot’s point of view. 

One such procedure requires tracking the target 
with the fixed cross for one-sixth of the initial slant 
range. It will be shown below that this results in 
approximately 12 per cent of the correct lead angle; 
let X = 0 . 12 X* (see Figure 16). 



Figure 16. Diagrammatic representation of orienta¬ 
tion of datum and sight lines in tracking the target 
during timing run. (For explanation of symbols, see 
text.) 


After tracking the target with the fixed cross for 
one-sixth of the initial slant range, let the dot be 
displaced to a symmetrical position on the other side 
of the line of the fixed cross, as shown in Figure 16. 
If the gyro axis remains fixed in space, a condition 
approximately realizable by turning off the range 
coils, the angle y between the new sight line and 
the gyro axis will be — 71 = 2Xo — 70 = (2 — a)Xo, 
and the new lead angle will be 


= - ^ (0.12)X*^ 0.68X*. 

a 

If the dot is displaced to a position twice as far on 
the other side of the fixed cross, the new lead angle 
X 2 will be 

X 2 = - (0.12)X*^0.96X*. 

a 


ing a larger initial value of Xq. The solution obtained 
as a function of the slant range tracking fraction 
will now be obtained. 

With Figure 17 for reference, the differential 
equation which the sight solves when tracking with 
the fixed cross will be derived. 



Figure 17. Diagrammatic representation of orientation 
of datum and sight lines in tracking with fixed cross. 
(For explanation of symbols, see text.) 


Here Six = —17 sin a and o- = a /- X. 

Hence 

. . j • FesinQ: . Ve . , 

o-=a; + X= X— ---= X-sin (a- — X), 

s s 

or, using equation ( 12 ) in the approximate form, 
V 

X* = — sin cr, 

F 

+ ( 17 ) 

Combination of equations (17) and ( 8 ) so as to 
eliminate a yields 




i)x = D! 

u/ s 


(18) 


where the term (Fg cos o-)/>S is less than Ve/S while 
l/w > 1/15. For this reason the term inF, will 
be omitted, leaving 


(1 - a)X + - = 

u S 


or, since 


X = >S —F—, 
dS dS 


it follows that 
d\ 




dS u(l — a)V {1 — a) S 


(19) 


It also is possilile to track with the fixed cross for a The solution of equation (19) which reduces to 
larger fraction of the original range, thus accumulat- XowheniS = *80 is 


X — XqC 


So-s s r 1 

u(l-a)F q- e u(l-a)F / ^ e'^— 

I - a U ua-a)V ^ 




( 20 ) 






















174 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


This solution is not capable of being represented in 
closed form by means of elementary functions, and 
the integrals are written with infinity as a limit 
because the exponential integral 

I.-/ N r -x(Jx 
— El { — z) = e — 

J z X 

is a tabulated function (for instance, the WPA 
“Tables of Sine, Cosine, and Exponential Integrals”). 
In the terms of Ei{ —z) equation (20) is 

X = Xoe-(^“- Ei{- z)Ei {- 20)] , 

(21) 

where 

N 

^ “ w(l -a)V ' 

If *S/*So = p, the quantity 1 — p = {So — S)/So is 
called the tracking ratio. Suppose Xo = 0 and 
X/X* = 0.1. Then from equation (21) 

- Ei {- 2 ) + Ei{- zo) = (22) 

This is the relation between 2 and Zo, i.e., between S 
and >So, which makes X/X* = 0.1. Table 2 shows a set 
of values of z and Zq which satisfy equation (22) 
together with the corresponding values of p and 
1 — p. From this table it is seen that a 15 per cent 
change in slant range results in an accumulation 
of 10 per cent of the desired lead angle. 


Table 2. Fraction of initial slant range for which 
10 per cent of the desired lead angle is obtained when 
tracking with fixed cross in Mark 23 sight. 


z 

Zo 

P 

1 - P 

0.2 

0.231 

0.865 

0.135 

0.4 

0.464 

0.863 

0.137 

0.6 

0.697 

0.861 

0.139 

0.8 

0.932 

0.859 

0.141 

1.0 

1.168 

0.856 

0.144 

1.2 

1.405 

0.854 

0.146 

1.4 

1.644 

0.852 

0.148 

1.6 

1.884 

0.849 

0.151 

1.8 

2.127 

0.846 

0.153 

2.0 

2.371 

0.844 

0.156 


For an estimation of the per cent of required 
solution obtained as function of the fraction of the 
initial slant range during which the solution is 
computed. Table 3 is useful. It gives values of 


X/X* for various values of 1 — p and for 2 = 1.0 and 
2 = 0.3. 


Table 3. X/X* as a function of tracking ratio. 


1 -P 

0.144 

0.167 

0.305 

0.5 

0.7 

0.9 


X/X* 

0.100 

0.116 

0.209 

0.324 

0.392 

0.417 

z = 1.0 

X/X* 

0.105 

0.124 

0.240 

0.426 

0.648 

0.843 

z = 0.3 


It should be noted that for V = 500 feet/sec, 
u = 15 sec, and a = —0.43, the value 2 = 1.0 
corresponds to a slant range at the end of the track¬ 
ing run of 10,700 feet, while 2 = 0.3 corresponds to a 
slant range of 3,200 feet for the same values of 
I', u, and a. 

Table 3 shows also that for small values of the 
tracking ratio 1 — p, the per cent of solution ob¬ 
tained is relatively independent of 2 , while for large 
tracking ratios more of the solution is obtained for 
small values of 2 . From the definition of 2 it is seen 
that 2 can be made small b}^ decreasing S, increasing 
u and F, and decreasing a, i.e., making a more 
negative. For instance, if a = —1, then 2 = 0.3 
corresponds to = 4,500 feet, V = 500 feet/sec,, 
and u = 15 sec. If 1 — p is taken as 0.5, then 
So = 9,000 feet, 2 o = O.G, and 

- = ~ [ - Ff( -0.3) + Ei{ -0.6)] = 0.305. 

X* 2 

If, at the end of this tracking run, the dot is dis¬ 
placed to the symmetrical position on the other side 
of the fixed cross, the lead angle which will be ob¬ 
tained will be 0.91X*. Again, if a = —0.43, So = 9,000 
feet, >S = 4,500 feet, u = 6.3 seconds, and V = 500 
feet/sec, then 2 = 1, X = 0.324 X* and the transposi¬ 
tion of the dot to the symmetrical position on the 
other side of the cross results in a lead angle of I.IX*. 
Various other operational combinations can, of 
course, be established. 

The amount of correction obtained by tracking^ 
with a free gyro, using the optical linkage of the 
Mark 23, will now be determined. This is nearly the 
situation when tracking with the gyro pip of the 
sight with the range coils turned off. 

Let r (see Figure 18) be the angle between the 
gyro axis and the horizontal at the instant when the 
gyro becomes free, i.e., the range coils are turned off. 
The gyro axds will retain this orientation in space. 



















USE OF THE LEAD-COMPUTING SIGHT 


175 


From Figure 18, it is seen that, since 7 is negative, 
r = 0- — 7 = 0-0 — 7o, (23) 

where ao and 70 are initial values. By use of equa¬ 
tion ( 6 ), equation (23) becomes 

n(Xo — X) = (To — cr, 

whence 

aX = (T. (24) 

It should be noticed that equation (24) is equiva¬ 
lent to equation ( 8 ) when u is extremely large, which 


It is seen from Table 4 that a large part of the 
solution Would bo obtained for a tracking ratio of 0.3 
if friction could be reduced to a negligible amount 
in the Mark 23. This would be especially true if 
an optical linkage constant of a = —0.215 were 
feasil)le. 


Wind Correction 



Figure 18. Diagrammatic representation of orientation 
of datum and sight lines in tracking while gyro is free. 


is possible only if frictional forces are made negligible. 
Taking a from the second of equation (11), equation 
(24) becomes 


aX = 


V sin X — Vg sin o- F ^ 

- = — (X — X*). 

>8 .8 


(25) 


If equation (25) is associated with the approximate 
equation V = dS/dt, the elimination of the quantity 
dt leads to the differential equation 


f/x X ^ X* 


(2G) 


The solution of this equation is 

or, if Xo = 0 , 

/N \ -1 _i 

= 1 — p a ^ 




(27) 


X* v8oy 

Table 4 shows how X/X* varies with the tracking 
ratio 1 — p for a = —0.43 and a = —0.215. 


Two other possibilities involving the rate of turn 
of the airplane caused by the use of the Mark 23 
may be considered. As has been shown in Section 
6.6.9, the range-wind correction obtained from the 
photoelectric accelerometer is of the order of 30 per 
cent.^^ If the rate of turn of the airplane were in¬ 
creased by a factor of 3, the total wind correction 
would be obtained. At the instant of uncaging the 
gyro, the airplane begins turning at a rate 3.33 times 
as fast as the sight line turns, and the whole wind 
correction would result if this rate of turn were 
continued for one-sixth of Tg. However, as the 
tracking ratio increa.ses, and the airplane approaches 
the collision course lead angle, the rate of turn 
decreases as lead angle is accumulated. The net 
effect has been investigated in reference 105, with 
the conclusion that approximately 65 per cent wind 
correction will result from the increased rate of turn 
of the airplane. 

The other po.ssibility concerns the crosswind 
approach. In reference 209 it is shown that in a 
cross wind approach, the angle of bank is such that 
the bomb is given a component of velocity in a 
direction parallel to wind direction, sufficient to 
give approximately 50 per cent Avind correction. 
It is as.sumed in this analysis that bomliing is accom¬ 
plished Avithout slipping or skidding. If the rate of 
turn of the airplane could be increased liy a factor 
of tAA’o, the angle of bank should be correspondingly 
increased so that the entire AA'ind correction Avould 


Table 4. X/X* for a free gyro (Xo = 0 ) with the Mark 23 optical linkage. 


1 - p 

0 1 

0,144 

0.167 

0.305 

0.5 

0.7 

09 


p-1 a 

0.783 

0.697 

0.654 

0.429 

0.199 

0.061 

0.0047 

a = - 0.43 

X/X* 

0.217 

0.303 

0.346 

0.571 

0.801 

0.939 

0.995 


p-l/a 

0.613 

0.485 

0.427 

0.184 

0.040 

0.004 


a = - 0.215 

X/X* 

0.387 

0.515 

0.573 

0.816 

0.960 

0.996 



















176 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


be obtained. The possibility of increasing the air¬ 
craft’s rate of turn by a suitably designed LCS is 
immediately evident. 

A AVord of caution is necessary v ith respect to the 
interpretation of the theoretical re.sults presented 
here. The lead angle and the angle involved in 
tracking with an LCS are quite small. Conse¬ 
quently, pilot aiming accuracy becomes quite im¬ 
portant, since small changes in the pilot’s aim may 
cause “wander” in the flight attitude of the aircraft, 
thus masking to a considerable extent the “intelli¬ 
gent” part of the LCS output. The feasibility of 
using the LCS in bomb tossing had not been tried in 
field tests at the end of the war. 


ANALYTICAL REDUCTION 
OF SYSTEMATIC ERRORS; 
REVISION OF THE FUNCTION^ 


Introduction 

In the course of the development of the bomb 
tossing technique, there has appeared and reap¬ 
peared the problem of elimination or reduction of 
systematic errors, i.e., errors following known phys¬ 
ical laws, as opposed to random errors. The fact 
that the angle of attack is not constant, for example, 
calls for a standardized flight calibration procedure; 
the effect of air resistance must be allowed for; the 
formulas valid for small pull-up angles require revi¬ 
sion for larger pull-ups. The general problem is, in 
fact, equivalent to that of revising the theory to take 
into account secondary physical phenomena neg¬ 
lected in the original basic assumptions. 

The method used most frequently in Mark 1 
equipment for reduction of errors is that of manual 
setting of the MPI adjustment dial (Section 6.4.9) 
which produces a change in the effective input time 
(time-to-target) Tc and consequently alters the 
pull-up time Tp. The chief disadvantages of this 
method are as follows: 


c Section 8.4 was written by S. 11. Lachenbruch of the 
Ordnance Development Division of the National Bureau of 
Standards. It covers work initiated under Division 4 sponsor¬ 
ship but completed after the toss bombing project was taken 
over by the Navy. For this reason the development of the 
theory is not given in as much detail as the treatment in 
Chapter 6. It was considered pertinent to include the 
essential results because of their importance to the project. 
Reference is made to source material “®for further <lerivation 
of the functions used. 


1. The proper value of the setting depends gener¬ 
ally on such unpredictable parameters as altitude 
and dive angle, and is usually very sensitive to 
changes in such parameters. 

2. ^Vllen the MPI adjustment is determined 
according to a formula designed for average condi¬ 
tions, departures from the average often yield large 
errors. 

3. The magnitude of the total required adjustment 
often exceeds the maximum attainable dial setting. 

4. The ]\IPI dial was primarily intended for 
special adjustments to meet conditions not encoun¬ 
tered in the general case, or to correct for extreme 
departures from average conditions. \Mien system¬ 
atic errors, which always affect the impact according 
to a definite law, are not elsewhere allowed for, the 
]MPI setting is no longer a special adjustment, but 
rather a required step whose omission always causes 
biased results. 

In Section 8.4.1 a method of systematic error 
correction is developed with the aim of eliminating or 
minimizing these disadvantages, i.e., (1) rendering all 
manual settings dependent only on known or pre¬ 
dictable quantities, so that an accurate setting may 
be made prior to each flight, (2) reducing greatly the 
effect of errors of estimation of these quantities, 
(3) reducing the total required adjustment to a 
magnitude which is always well within instrumental 
limits, and (4) incorporating the major portion of 
the correction in the lwml3 director itself {\p func¬ 
tion), so that the MPI adjustment need be u.sed only 
as a secondary correction for deviations from average 
conditions. The theoretical implications of this 
method, namely, that the systematic errors in ques¬ 
tion are automatically eliminated (except for small 
second-order errors) for average values of the known 
or predictable quantities, that such errors are so 
greatly reduced for all values that the manual adjust¬ 
ment is generally optional, and that use of the latter 
generally reduces the errors to almost negligible 
magnitude, remain to be put to practical test. 

In bomb tossing the pull-up time Tp is determined 
according to a formula of the form [cf. equation (19) 
of Chapter 2]: 


' F{K) 


(28) 


where is the time-to-target. 

F{K) is a function of the normal pull-up accelera¬ 
tion Kg, and of its mode of variation with time; and 
^ is chiefly a function of the dive angle a. The \J/ 






ANALYTICAL REDUCTION OF ERRORS OF THE 'I' FUNCTION 


177 


function also depends somewhat on Tc/T", T" being 
the airspeed, and in most bomb directors this varia¬ 
tion is taken into account by means of an airspeed 
dial which is preset (see Section 2.1.3). The varia¬ 
tion of x}/ with K is negligible. 

The method, whose mathematical derivation is 
given in reference 116, is applied to errors due to air 
resistance and to errors resulting from variation in 
angle of attack, l)ut may be extended to other system¬ 
atic errors. A brief outline of the method follows: 

1. The formula for the systematic error 5 in 
question is converted into a formula for the change 
ATp in Tp required to offset that error. 

2. Acpiantity e^, depending only on a and TJV, is 
determined such that when V and other predictable 
parameters assimie their average or modal values, 
changing xf/ by an amount X xp will change Tp by 
the amount ATp determined in (1), and therefore, 
theoretically eliminate the error in question for 
such modal values. This procedure is carried out for 
each systematic error in turn, and the corrections 

so determined are applied to the most accurate 
of the xp functions derived to date, yielding a revised 
xp function. 

3. To correct for departure of these parameters 


from their modal values, a quantity €<;, depending 
only on V and other known or predictable quantities 
such as ballistic coefficient, is determined such that 
changing by an amount e^X Tc w'ill eliminate most 
of the residual error not eliminated by revision of the 
xp function. This correction may be applied by means 
of the MPI adjustment dial prior to each flight, 
using the known values of the parameters involved. 

Thus, theoretically, the revision of the xp function 
completely offsets the systematic errors, for all 
values of a and TJV, and for modal values of V 
and other predictable parameters; and the AIPI 
adjustment in turn offsets the effect of deviations of 
these predictable parameters from their modal values. 

In addition to the corrections for air resistance and 
angle of attack by the method outlined above, 
corrections for large pull-ups and for nonconstant 
pull-up acceleration are made by means of relations 
derived in Chapter 6. 

8.4.2 xhe Revised ip Function (ipr) 

The new' theoretical xp function, as derived in 
reference 116, is given by 

TJV) = Xpeil + e^.ar + ^-aa) + /2g\ 

= l/'e + Aar + ^aa ”1" 



cC 


Figure 19. Revised xp function (xpr) versus a, for different values of Tc/V ( = 0.01, 0.03, and 0.05). For purposes of 
comparison, the xpe function versus a is given by dashed lines for Tc/V = 0.01 and 0.05. 





178 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


where 

\pe is the ^ function resulting from the exact solu¬ 
tion of the toss bombing equations for circular 
pull-up {ypg is derived, tabulated, and plotted in 
Sections 6.1.3, 6.1.4, and 6.1.5), 

A* is a correction term to allow for nonconstant 
pull-up acceleration, 

Aar = c^.ar is ^11 allowance for the effect of air 
rcsi.stance on the bomb,®®’^^® and 

^aa = ^■aa'Pe is a similar allowance for variation 
in angle of attack. 

The quantities e^.ar and e^.^a are given by the 
following equations: 

= {VVc)-b^c-_a- TJV (30) 

€^.aa = (^71,000 F2). 

(cos a — COS a)/sin a (31) 
where 6p, hpc and a are functions of Tc/V and a, and 
the barred symbols represent mean values, and there¬ 
fore constants. Here c is an average bomb ballistic 
coefficient, and CW is the average value of a coeffi- 
'cient determining a plane’s rate of change of angle 
•of attack. 


The revised theoretical i/' function (\pr) is plotted in 
Figure 19 as a function of a for different values of 
TJV, and is tabulated in Table 5. 


T.\ble 5. Values of if/r (K =3). 



0.01 

0.02 

0.03 

0.04 

0.05 

10 ° 

1.054 

1.063 

1.097 

1.162 

1.295 

20 ° 

0.973 

0.962 

0.971 

0.995 

1.045 

CO 

o 

0.872 

0.852 

0.845 

0.847 

0.856 

40° 

0.747 

0.726 

0.711 

0.701 

0.689 

50° 

0.603 

0.584 

0.567 

0.553 

0.543 

60° 

0.438 

0.432 

0.419 

0.406 

0.395 


In the evaluation of \pr, K has been set equal to a 
modal value = 3, except in the term Ak which is 
evaluated from reference 93. The variation of \pr 
with K is generally negligible. No calculations have 
been made for dive angles beyond the operating 
extremes of 10 and 60 degrees. In fact, an absurd 
result is obtained at ct = 0 degrees, at which Aaa 
and therefore 4/r are infinite. 


.01 



a: 


Figure 20. Correction terms added to to obtain xpr, plotted versus dive angle for different values of Tc/V. A^ is prac- 
ticalh' independent of Tc/V. 




















ANALYTICAL REDUCTION OF ERRORS OF THE FUNCTION 


179 


By comparison it is seen that the curves of Figure 
18 are appreciably denser than any of the sets of 
earlier i/' curves (see Figure 2, Chapter 2, and 
Section 6.1), at least for dive angles greater than 
20 degrees. In other words is less dependent on 
TJV than were the earlier xp functions. 

Each of the correction components A^r, Aaa, and 
Ak is plotted separately in Figure 20. The xp^ function 
of Figure 19 has been obtained by adding all these 
components to the xpg function of Section 6.1.3. 

An important consequence of the use of the xp^ 
function as a base (to which the three correction 
terms are applied) is the removal of all range limita¬ 
tions imposed by the so-called 100-foot error curves of 
Figure 11 of Chapter 2, and Figure 7 of Chapter 6, 
which result from approximations implicit in the 
xpo and xpi functions, and which have been used as 
criteria determining operating limits. 

The degree to which systematic errors are reduced 


by the revision of the xp function is discussed in 
reference 116. 

In designing a gyro potentiometer xp card based 
on a given theoretical xp function, the usual procedure 
is to fit the xp curve for a modal value of TJV by 
means of a series of straight line segments, thus 
obtaining an instrumental \p function which may be 
made to vary instrumentally with Tc/V in a manner 
comparable with theory. The complete procedure, 
involving calculation of voltages according to expo¬ 
nential formulas, is outlined in Section 6.3 for the 
xpi function. 

In the instrumentalization of the xp^ function there 
is some leeway in the choice of a modal value of 
TJV. A value 7VF = 0.025, however, would be 
the choice most consistent with the remainder of the 
theory. This is the value of TjV used in all formulas 
given here, being based on a modal slant range 
S = 7,500 feet and a modal air speed V = 325 knots 


T.\ble 6. Values of supplementary MPI adjustments for air resistance (f-c-ar) (for use with xp,. function). 


\ True air- 
\ speed 
\ knots 
Bal-\ 
listic \ 
coeff. \ 
(c) \ 

225 

250 

275 

300 

325* 

350 

375 

400 

425 

450 

475 

Recip¬ 

rocal 

1/c 


% 

% 

% 

% 

% 

% 

% 


% 

% 

% 


% 


0.75 

+ 3.1 

+ 5.0 

+ 7.1 

+ 9.4 

+ 

11.9 

+ 

14.6 

+ 

17.6 

+ 

20.7 

+ 

24.0 

+ 

27.6 

+ 

31.3 

1.33 

1.00 

+ 1.0 

+ 2.5 

+ 4.0 

+ 5.8 

+ 

7.7 

+ 

9.7 

+ 

11.9 

+ 

14.2 

+ 

16.7 

+ 

19.4 

+ 

22.2 

1.00 

1.25 

— 0.2 

+ 0.9 

+ 2.2 

+ 3.6 

+ 

5.1 

+ 

6.7 

+ 

8.5 

+ 

10.4 

+ 

12.4 

+ 

14.5 

+ 

16.7 

0.80 

1.50 

— 1.0 

— 0.1 

+ 1.0 

+ 2.1 

+ 

3.4 

+ 

4.8 

+ 

6.2 

+ 

7.8 

+ 

9.5 

+ 

11.2 

+ 

13.1 

0.67 

1.75 

— 1.6 

— 0.8 

+ 0.1 

+ 1.1 

+ 

2.2 

+ 

3.4 

+ 

4.6 

+ 

5.9 

+ 

7.4 

+ 

8.9 

+ 

10.5 

0.57 

2.00 

— 2.0 

— 1.3 

— 0.5 

+ 0.3 

+ 

1.3 

+ 

2.3 

+ 

3.4 

+ 

4.6 

+ 

5.8 

+ 

7.1 

+ 

8.5 

0.50 

2.25 

— 2.4 

— 1.7 

— 1.0 

— 0.3 

+ 

0.6 

+ 

1.5 

+ 

2.5 

+ 

3.5 

+ 

4.6 

+ 

5.8 

+ 

7.0 

0.44 

2.50* 

— 2.7 

— 2.1 

— 1.5 

— 0.8 


0.0 

+ 

o 

00 

+ 

1.7 

+ 

2.6 

+ 

3.6 

+ 

4.7 

+ 

5.8 

0.40 

2.75 

— 2.9 

— 2.4 

— 1.8 

— 1.2 

— 

0.5 

+ 

0.3 

+ 

1.1 

+ 

1.9 

+ 

00 

+ 

3.8 

+ 

4.8 

0.36 

3.00 

— 3.1 

— 2.6 

— 2.1 

— 1.5 

— 

0.9 

— 

0.2 

+ 

0.6 

+ 

1.3 

+ 

2.2 

+ 

3.1 

+ 

4.0 

0.33 

3.25 

— 3.2 

— 2.8 

— 2.3 

— 1.8 

— 

1.2 

— 

0.6 

+ 

0.1 

+ 

00 

d 

+ 

1.6 

+ 

2.4 

+ 

3.3 

0.31 

3.50 

— 3.4 

— 3.0 

— 2.5 

— 2.0 

— 

1.5 

— 

0.9 

— 

0.2 

+ 

0.4 

+ 

1.1 

+ 

1.9 

+ 

2.7 

0.29 

4.00 

— 3.6 

— 3.2 

— 2.8 

— 2.4 

— 

1.9 

— 

1.4 

— 

0.9 

— 

0.3 

+ 

0.4 

+ 

1.0 

+ 

1.7 

0.25 

4.50 

— 3.7 

— 3.4 

— 3.1 

— 2.7 

— 

2.3 

— 

1.8 

— 

1.3 

— 

0.8 

— 

0.3 

+ 

0.3 

+ 

1.0 

0.22 

00 

— 5.1 

— 5.1 

— 5.1 

— 5.1 

— 

5.1 

— 

5.1 

— 

5.1 

— 

5.1 

— 

5.1 

— 

5.1 

— 

5.1 

0.00 


•Modal values as used in > 1 /^ calculations. 























180 


DEVELOPMENT OF IMPROVED TOSSING EQUIPMENT 


Furthermore, the \pr curve for that value (very- 
close to the 0.03 curve of Figure 19) has only slight 
curvature, so that it may be fitted satisfactorily with 
relatively few line segments — probably only two. 

8.4.3 MPI Adjustment 

The components e^.ar and e^.aa of the \pr function 
do not represent a theoretically complete correction 
for air resistance and angle of attack variation unless 
all the known or predictable quantities V, c, CW 
assume their mean or modal values. Deviations from 
such means may be corrected by setting the MPI 
adjustment dial in an amount which depends on 
these quantities and which may therefore be evalu¬ 
ated from known or predicted values of these quan¬ 
tities prior to each flight. 

A fixed setting of the MPI adjustment dial 
causes a fixed fractional or per cent change 
= ATJTc in the effective value of T^, the calibra¬ 
tions on the dial being proportional to (see 
Section 6.4). 


The optimum valees of the MPI setting e<,.ar for 
use in conjunction with the \pr function to offset the 
effect of air resistance are tabulated in Table 6 for 
different values of V and c. Similarly Table 7 gives 
the values of the MPI setting e^.aa nsed to offset 
angle of attack variations, for different values of 
V and CTF. The values of C and the nominal (aver¬ 
age) values of IF are tabulated for several types of 
planes in Table 8. The optimum net or total adjust¬ 
ment for these two sources of error is t^-ar + ^c-aa- 
In equation form, as derived in reference 116, these 
terms are 



The use of the tables to determine the MPI adjust¬ 
ment is illustrated by the following example: A 
TBM plane at nominal weight, whose bomb director 
operates according to the ypr function, is about to 
toss a bomb whose ballistic coefficient is 3.0, \\ith a 


Table 7. Values of supplementary MPI adjustment for angle of attack variation ( ec.aa)- 
(For use with \pr function.) 


True air- 
N, speed 

knots 

CTF 

225 

250 

275 

300 

325* 

350 

375 

400 

425 

450 

475 


% 

% 

% 

% 

% 

% 

% 

% 

% 

% 

% 

1.4 X 106 

+ 7.4 

+ 

4.7 

+ 2.7 

+ 1.2 

0.0 

— 0.9 

— 1.7 

— 2.3 

— 2.8 

— 3.3 

— 3.6 

1.6 

+ 8.5 

+ 

5.4 

+ 3.1 

+ 1.4 

0.0 

— 1.1 

— 1.9 

— 2.7 

— 3.2 

— 3.7 

— 4.2 

1.8 

+ 9.5 

+ 

6.1 

+ 3.5 

+ 1.5 

0.0 

— 1.2 

— 2.2 

— 3.0 

— 3.6 

— 4.2 

— 4.7 

2.0 

+ 10.6 

+ 

6.7 

+ 3.9 

+ 1.7 

0.0 

— 1.3 

— 2.4 

— 3.3 

— 4.1 

— 4.7 

— 5.2 

2.2 

+ 11.7 

+ 

7.4 

+ 4.3 

+ 1.9 

0.0 

— 1.5 

— 2.7 

— 3.6 

— 4.5 

— 5.1 

— 5.7 

2.4* 

+ 12.7 

+ 

8.1 

+ 4.6 

+ 2.0 

0.0 

— 1.6 

— 2.9 

— 4.0 

— 4.9 

— 5.6 

— 6.2 

2.6 

+ 13.8 

1 

+ 

8.7 

+ 5.0 

+ 2.2 

0.0 

— 1.7 

— 3.2 

— 4.3 

— 5.3 

— 6.1 

— 6.8 

2.8 

+ 14.8 

+ 

9.4 

+ 5.4 

+ 2.4 

0.0 

— 1.9 

— 3.4 

— 4.6 

— 5.7 

— 6.5 

— 7.3 

3.0 

1 +15.9 

+ 10.1 

+ 5.8 

+ 2.5 

0.0 

— 2.0 

— 3.6 

— 5.0 

— 6.1 

— 7.0 

— 7.8 

3.2 

+ 17.0 

+ 10.8 

+ 6.2 

+ 2.7 

0.0 

— 2.2 

— 3.9 

— 5.3 

— 6.5 

— 7.5 

— 8.3 

3.4 

+ 18.0 

+ 11.4 

+ 6.6 

+ 2.9 

0.0 

— 2.3 

— 4.1 

— 5.6 

— 6.9 

— 7.9 

— 8.8 

3.6 X 106 

+ 19.1 

+ 12.1 

+ 7.0 

+ 3.0 

0.0 

— 2.4 

— 4.4 

— 6.0 

— 7.3 

— 8.4 

— 9.3 


‘Modal values as used in calculations. 





















ANALYTICAL REDUCTION OF ERRORS OF THE ^ FUNCITION 


181 


true airspeed of approximately 275 knots in the dive. 
From Table S, C = 132 and TF = 15,500 lb, hence 
CW = 2.05 X 106. Also c = 3.0 and V = 275 
knots. With V = 275 knots and c = 3.0, Table G 
gives €<..ar = —2.1 percent. Similarly, with T" = 275 
knots and CTF = 2.05 X 10® (interpolating between 
2.0 and 2.2), Table 7 gives ec.aa = +4.0 per cent. 
Hence the optimum net MPI adjustment is 
— 2.1 +4.0 = +1.9 per cent. 


Table 8 . Aircraft coefficients (C) and nominal weights 
(TF) of most frequently used planes, 


Plane 

c* 

Nominal 

ir (lb) 

Nominal 

CTT^ 

Nominal 

CW - CT’ 

F4U (FG) 

227 

12,000 

2.72 X 10® 

+ 0.33 X 10® 

SB2C 

165 

15,000 

2.47 

+ 0.08 

F6F 

193 

12,400 

2.39 

0.00 

TBM (TBF) 

132 

15,500 

2.05 

- 0.34 

FiM (F4F) 

250 

7,500 

1.87 

- 0.52 

P-38 L 

205 

17,200 

3.53 X 10® 

+ 1.14 X 10® 

P-51 K 

350 

9,500 

3.32 

+ 0.93 


*C appears in the formula: 

cos a 

Angle of attack = CW y2 ~ k, 

and is here tabulated in units corresponding to angle of attack in mils, 
W in pounds, and V in knots. 

Examination of Tables 6 and 7 and equations (32) 
and (33) indicates that all four of the disadvantages 
cited in Section 8.4.1 are theoretically overcome 
under this system. It is to be noted that ec-ar and 
«c-aa vary in opposite directions with V, thus impos¬ 
ing an additional limit on the magnitude and degree 
of variation of their sum. 

Advantages and Comments 

The revision of the function — with optional 
MPI adjustment — appears to be a considerably 
more effective method of correcting for systematic 
errors than purely manual adjustment methods. 
The effectiveness of the method in practice remains 
to be determined from experiments involving the 
design and installation of a revised ^ card, its testing 


in the field, and a rigid statistical analysis of the 
results. 

The formulas and curves so far derived*^® may be 
somewhat improved upon by revising the modal 
values, from which calculations were made, to fit 
actual conditions more closely. The possibility of 
fitting a somewhat different function to each type 
of plane, based on the value of C and the average 
values of IF and V for such plane, might also be 
considered. The correction terms in \f/r plotted 
separately in Figure 20 facilitate the adjustment of 
any single term. 

It has been found that reasonable changes in the 
assumed modal values V, c, CW may cause appre¬ 
ciable changes in the density of the ^pr curves, i.e., 
in the dependency of ypr on TJV. Since, further¬ 
more, the MPI adjustment may be used to offset 
deviations from such modal values, the question 
arises as to whether some reasonable combination of 
values F, c, and CW might render xp^ practically 
independent of TJV, making it a function of a 
alone. This w'ould be especially advantageous in 
bomb directors such as the Mark 3. It has been 
noted that \pr is itself considerably less dependent on 
TJV than \po, xpi srndxpe. 

The extension of the method to include other 
systematic errors, such as that due to nonconstant 
airspeed in the dive, is entirely feasible. Such exten¬ 
sion would involve an additional correction term in 
the \pr function, and an additional MPI adjustment 
table. 

Furthermore, systematic errors w'hich depend on 
the pull-up acceleration K, may be offset by revision 
of the F{K) function for average values of other 
parameters, since 1/F, like \p and T^, is a factor of 
Tp, and the analysis in reference 116 may be extended 
to include changes in this factor. 

One important consequence of this method of 
correction is a greatly simplified flight calibration 
procedure (see Chapter 4), When the \pr function is 
used, an accurate sight setting may be attained by 
(1) adjusting the MPI dial according to Tables 
6 and 7, and (2) tossing bombs at any convenient 
range, at an airspeed as close as possible to 325 
knots, and at a dive angle of at least 15 degrees (at 
least 20 degrees if 325 knots cannot be approximated 
closely; actually somewhat higher dive angles will 
yield more accurate results) — and adjusting the 
sight after each such run until impact is consistentl}" 
near the target. The errors at other values of S, 
a, and V will be very slight. 




















v; 






11 

* ■ rsW ^ 


% 





< 4 * 





/ 



» 


% 




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BIBLIOGRAPHY 


Numbers such as Div. 4-326.3-Ml indicate that the document has been microfilmed and that its 
title appears in the microfilm index printed in a separate volume. For access to the index volume 
and to the microfilm, consult the Army or Navy agency listed on the reverse of the half-title page. 


XDRC ARMOR AXD ORDXAXCE REPORTS 

1. A Preliminary Analysis of the Effect of Air Resistance on 

Certain Aspects of 'Toss Bombing, S. H. Lachenbruch, 
OSllD 4589, Service Projects AC-62 and NO-185, 
Report A-308, NBS, Ordnance Development Division, 
September 1944. Div. 4-312.5-Ml 

XDRC DIVJSIOX 4 — NBS REPORTS 

2. Test of Integrating Accelerometers at Aberdeen, February 

27, 1943 , F. R. Kotter, NDRC-4, Service Project OD-27, 
Memorandum Report 98-T, NBS, Ordnance Develop¬ 
ment Division, Mar. 17, 1943. Div. 4-326.3-Ml 

3. Test of Bomb Release Mechanism, William B. iMcLean 

and Jacob Rabinow, NDRC-4, Service Project OD-27, 
Memorandum Report 4S, NBS, Ordnance Development 
Division, Mar. 19, 1943. Div. 4-328.5-Ml 

4. Tests of Accelerometers at Aberdeen, March 12, 1943, F. R. 
Kotter and T. C. Hellmers, NDRC-4 Service Project 
OD-27, Memorandum Report 112-T, NBS, Ordnance 
Development Division, Mar. 23, 1943. Div. 4-326.3-M2 

5. Mathematical Investigation of Some Phases of Toss Bomb¬ 

ing, Phillip R. Karr, NDRC-4, NBS, Ordnance Develop¬ 
ment Division, Mar. 26, 1943. Div. 4-311-Ml 

6. Test of Integrating Accelerometers, April 6, 1943 [Prelimi¬ 
nary Report], F. R. Kotter, NDRC-4, Service Project 
OD-112, Memorandum Report 152-T, NBS, Ordnance 
Development Division, Apr. 10, 1943. Div. 4-326.3-M3 

7. Test of Mechanical Integrating Accelerometer, D. A. 
Worcester and R. Kotter, NDRC-4, Service Project 
OD-112, Memorandum Report 166-T, NBS, Ordnance 
Development Division, Apr. 15, 1943. Div. 4-326.3-M4 

8. Toss Bombing: Acceleration-Integrator Bomb Release, 

William B. McLean, William L. Whitson, and Jacob 
Rabinow, NDRC-4, Service Project AC-62, Memoran¬ 
dum Report 5S, NBS, Ordnance Development Division, 
May 16, 1943. Div. 4-324.11-Ml 

9. Toss Bombing: Compensating Acceleration-Integrator 
Bomb Release, Including Field Test Data, William B. 
McLean and William L. Whitson, NDRC-4, Service 
Project AC-62, Memorandum Report 7S, NBS, Ord¬ 
nance Development Division, Aug. 14, 1943. 

Div. 4-324.11-M2 

XBS REPORTS 

10. Toss Bombing Tests at Cedar Point Xaval Air Station, 
Oct. 9-Xov. 4, 1943 , F. R. Kotter, Report OD-1-57, NBS, 
Ordnance Development Division, Nov. 18, 1943. 

Div. 4-330-Ml 

11. Toss Bornbing: Summary of Proof Data, William B. 
McLean and William L. Whitson, Report OD-4-10, 
NBS, Ordnance Development Division, Nov. 30, 1943. 

Div. 4-311-M3 


12. Displaced-Image Rangefinder Goggles, William L. Whit¬ 

son, Report OD-4-33, NBS, Ordnance Development 
Division, Feb. 14, 1944. Div. 4-720-Ml 

13. Toss Bombing Field Data Using ,1 YF Altimeter and Gyro 

Dive Angle Attachment, William L. Whitson, Report 
OD-4-34, NBS, Ordnance Development Division, Feb. 
14, 1944. Div. 4-330-M2 

14. Toss Bombing Field Data Using A YF Altimeter and Gyro 

Dive Angle Attachment, William L. Whitson, Report OD- 
4-39, NBS, Ordnance Development Division, Mar. 16, 
1944. Div. 4-330-M2 

15. Toss Bombing Tests at Patuxent, William L. Whitson, 

Report OD-4-64, NBS, Ordnance Development Divi¬ 
sion, May 10, 1944. Div. 4-330-M3 

16. Reversing Integrator with Hyperbolic Slidewire, William L. 

Whitson, Reiiort OD-4-57, NBS, Ordnance Develop¬ 
ment Division, May 22, 1944. Div. 4-324.12-Ml 

17. Toss Bombing Tests at Patuxent Using Kollsman Alti¬ 

meter in SB2C-3 Plane, William L. Whitson, Report 
OD-4-67, NBS, Ordnance Development Division, May 
25, 1944. Div. 4-330-M4 

18. Toss Bombing Tests at Patuxent Using Kollsman Alti¬ 

meter in SB2C-3 Plane, William L. Whitson, Report 
OD-4-70, NBS, Ordnance Development Division, May 
29, 1944. Div. 4-330-M4 

19. Dive Toss Bombing, William L. Whitson, Report OD-4- 
58, NBS, Ordnance Development Division, June 1, 1944. 

Div. 4-311-M4 

20. Field Test, Toss-Bornbing, Patuxent, June 23, 1944, D. C. 

Friedman, Report OD-1-401, NBS, Ordnance Develop¬ 
ment Division, July 14, 1944. Div. 4-330-M5 

21. Toss Bombing with a TBM Airplane Using a Fixed-Time 
Integrator, F. R. Kotter, Report OD-TB-10, NBS, Ord¬ 
nance Development Division, Aug. 21, 1944. 

Div. 4-324.13-Ml 

22. The Use of a Reversing Electrical Integrator in Low Level 

Toss Bombing with a TBM Airplane, F. R. Kotter, 
Report OD-TB-15, NBS, Ordnance Development Divi¬ 
sion, Aug. 25, 1944. Div. 4-324.12-M2 

23. Toss Bombing ivith an F6F Airplane at the Xaval Proving 
Ground, Dahlgren, Va., F. R. Kotter, Report OD-TB-17, 
NBS, Ordnance Development Division, Aug. 25, 1944. 

Div. 4-330-M6 

24. Equations for Toss Bombing for the Horizontal Case 

Assuming Acceleration is a Function of Time, William B. 
McLean, Report OD-TB-19, NBS, Ordnance Develop¬ 
ment Division, Aug. 31, 1944. Div. 4-311.3-Ml 

25. Procedure for Altering and Rebalancing the Gyro, Frank E. 

Inman, Report OD-TB-21, NBS, Ordnance Develop¬ 
ment Division, Sept. 18, 1944. Div. 4-325.1-Ml 



183 


184 


BIBLIOGRAPHY 


26. Bridge for Checking Gyro Angle versus Voltage, Harold N. 

Cones, Report OD-TB-25, NBS, Ordnance Development 
Division, Sept. 21, 1944. Div. 4-325.1-M2 

27. Bridge for Adjustment of for Different Plane Velocities, 
Harold N. Cones, Report OD-TB-33, NBS, Ordnance 
Development Division, Sept. 28, 1944. Div. 4-312.2-Ml 

Addendum; Revised Computations of Gyro Output Volt¬ 
age at 40° Dive Angle for Different Plane Velocities, S. H. 
Lachenbruch, Report OD-TB-33A, NBS, Ordnance De¬ 
velopment Division, Oct. 25, 1944. Div. 4-312.2-M2 

28. Effect of Changing Integrator RC Ratio to Correct for an 

Error in Alignment of Sight With Line of Plight, William 
B. McLean, Report OD-SP-40, NBS, Ordnance Devel¬ 
opment Division, Oct. 26, 1944. Div. 4-312.1-Ml 

29. Variation of Integrator iff Function with Velocity, Neglect¬ 
ing Air Resistance, R. DeAmicis, Report OD-SP-41, 
NBS, Ordnance-Development Division, Nov. 14, 1944. 

Div. 4-312.2-M4 

30. Comparison between Actual and Theoretical Values of Out¬ 

put Voltage from Gyro Potentiometer, R. DeAmicis, 
Report OD-SP-42, NBS, Ordnance Development Divi¬ 
sion, Nov. 3, 1944. Div. 4-325-Ml 

31. Test Set for Measuring Closing Time of Relays, Harold N. 

Cones, Report OD-SP-43, NBS, Ordnance Development 
Division, Oct. 17, 1944. Div. 4-328.41-M2 

32. Analysis of Hortizontal Range Error Resulting from Neglect 
of Pull-up Angle, S. H. Lachenbruch, Report OD-SP-45, 
NBS, Ordnance Development Division, Nov. 7, 1944. 

Div. 4-311.1-M2 

33. Use of the 100-Ft Horizontal Error Curves for Errors of 
Other Magnitudes, S. H. Lachenbruch, Report OD-SP-46, 
NBS, Ordnance Development Division, Nov. 8, 1944. 

Div. 4-312.2-M3 

33a. Temperature Cycling of IRC BW-1 and Other Resistors, 
.A. E. Peterson and F. O. Harrer, Report OD-SP-47, 
NBS, Ordnance Development Division, Oct. 27, 1944. 

Div. 4-236-M5 

Addendum: Temperature Cycling of IRC BW-1 Resistors, 
Report OD-SP-47a, Nov. 28, 1944. Div. 4-236-I\I6 

34. General Toss Bombing Solution for the Case of a A'o?i- 
Constant Acceleration, Including the Effect of the Pull-up 
Angle, Albert London, Report OD-SP-48, NBS, Ord¬ 
nance Development Division, Nov. 3, 1944. 

Div. 4-311.1-Ml 

35. Relationship among Important Angles in Toss Bombing 
Trajectories, S. H. Lachenbruch, Report OD-SP-49, 
NBS, Ordnance Development Division, Nov. 10, 1944. 

Div. 4-311.1-M3 

36. Vibration Tests on Integrator During Actual Flights, 
Leroy R. Sweetman, Report OD-SP-50, NBS, Ordnance 
Development Division, Nov. 6, 1944. Div. 4-324.3-Ml 

37. Gun Sight Settmg on P-47 Airplane for Toss Bombing, 
William L. Whitson, Report OD-SP-51, NBS, Ordnance 
Development Division, Nov. 10, 1944. Div. 4-323.2-Ml 

37a. Report on Integrator Brushes and Commutator, Forest K. 
Harris, Report OD-SP-52, NBS, Ordnance Development 
Division, Nov. 15, 1944. Div. 4-324.22-Ml 


38. Measurements of Wind Velocity with the Directional Gyro, 
William L. Whitson, Report OD-SP-53, NBS, Ordnance 
Development Division, Nov. 22, 1944. Div. 4-312.4-Ml 

38a. Relay Tests, Harold N. Cones and F. O. Harrer, Report 
OD-SP-54, NBS, Ordnance Development Division, 
Nov. 22, 1944. Div. 4-328.41-M3 

39. Bomb Director Performance, Patuxent River Station, 
November 7-14, 1944, P> V. Johnson, Report OD-SP-55, 
NBS, Ordnance Development Division, Nov. 22, 1944. 

Div. 4-321.3-Ml 

40. Application of Toss Bombing E(piipment to Torpedo Toss¬ 
ing, Albert London, Report OD-SP-56, NBS, Ordnance 
Development Division, Nov. 28, 1944. Div. 4-340-M2 

41. Modified Kollsman Altimeter for Toss Bombing Equip¬ 
ment, B. L. Wilson and Arnold We.xler, Report OD-SP-58, 
NBS, Ortlnance Development Division, Dec. 2, 1944. 

Div. 4-322.1-Ml 

42. Determination of Proper RF Filter for the Thyratron in the 
Integrator, Joseph H. Hibbs, Report OD-SP-57, NBS, 
Ordnance Development Division, Dec. 4, 1944. 

Div. 4-324.22-M2 

43. Operation of Toss-Bombing Integrator Circuit, Albert 

London, Report OD-SP-60, NBS, Ordnance Develop¬ 
ment Division, Dec. 7, 1944. Div. 4-324.21-M2 

44. Setting of the Intervalorneter for Toss Bombing, S. H. 

Lachenbruch, Report OD-SP-61, NBS, Ordnance Devel¬ 
opment Division, Jan. 1, 1945. Div. 4-328.1-Ml 

45. Operating Time of Relay, Harold N. Cones, Report OD- 

SP-62, NBS, Ordnance Development Division, Dec. 7, 
1944. Div. 4-328.41-M4 

46. Bomb Director Performance, Patuxent River Station, 
November 15-25, 1944, P- V. Johnson, Report OD-SP-63, 
NBS, Ordnance Development Division, Dec. 8, 1944. 

Div. 4-321.3-Ml 

47. Effect of Variation in Dive Angle and Release Altitude on 
Bomb Director Operation in SB2C Planes, P. V. Johnson 
and John H. Park, Report OD-SP-65, NBS, Ordnance 
Development Division, Dec. 27, 1944. Div. 4-321.3-M2 

48. Progress of Development of Electrical Indicating Altimeter, 
Joseph IL Hibbs, Report OD-SP-66, NBS, Ordnance 
Development Division, Dec. 19, 1944. Div. 4-322.2-M2 

49. Introduction to Operation of Bomb Director, AN/ASG-10 
(XN), W. S. Hinman, Jr., Report OD-SP-67, NBS, Ord¬ 
nance Development Division, Dec. 15, 1944. 

Div. 4-321.1-Ml 

49a. Further Temperature Tests on Sprague Vitamin Q Capaci¬ 
tors, A. E. Peterson and F. O. Harrer, Report OD-SP-68, 
NBS, Ordnance Development Division, Dec. 16, 1944. 

Div. 4-328.3-Ml 

50. Bomb Director Performance, Patuxent River Station, 

November 28-December 7, 1944, P- A • Johnson, Report 
OD-SP-69, NBS, Ordnance Development Division, 
Dec. 16, 1944. Div. 4-321.3-Ml 

51. Tests on Effect of Aircraft Radio and Intercommunication 
System on Operation of Mk 1 Bomb Director, A. E. Peter¬ 
son ami C. Weaver Creed, Report OD-SP-71, NBS, 
Ordnance Development Division, Dec. 29, 1944. 

Div. 4-321.2-MI 



BIBLIOGRAPHY 


18o 


52. Effect of Variation in Dive Angle and Altitude of Release 
on Bomb Director Performance in an F6F-5 Airplane, 
John H. Park, Report OD-SP-72, NBS, Ordnance 
Development Division, Dec. 30, 1944. 

Div. 4-321.3-M3 

53. Bomb Director Performance, Patuxent River Station, 

December 8 to December 28, 1944, B. V. Johnson, Report 
OD-SP-73, NBS, Ordnance Development Division, 
Dec. 30, 1944. Div. 4-321.3-Ml 

54. Preliminary Report on the Photo-Electric Dive Angle 
Meter, William B. McLean, Joseph H. Hibbs, and McKay 

R. Bradley, Rejjort OD-SP-74, NBS, Ordnance Develop¬ 
ment Division, Jan. 8, 1945. Div. 4-327-M2 

54a. Temperature Cycling of Precision irtrc-iroand Resistors, 
December 30, 1944 to January 6, 1945, F. O. Harrer and 
Harold N. Cones, Report OD-SP-75, NBS, Ordnance 
Development Division, Jan. 11, 1945. Div. 4-236-M8 

55. Correction of the Acceleration Dilegrator for Air Resistance, 

S. H. Lachenbruch, Report OD-SP-76, NBS, Ordnance 
Development Division, Jan. 12, 1945. Div. 4-312.5-M2 

56. Tables of New if Functions and Other Related Quantities, 
C. F. Five and Albert London, Reixirt OD-SP-77, NBS, 
Ordnance Development Division, Jan. 15, 1945. 

Div. 4-312.2-M5 

57. A'ew if Card Design, Albert London and A. Fi. Willgoos, 

Report OD-SP-78, NBS, Ordnance Development Divi¬ 
sion, Jan. 17, 1945. Div. 4-312.2-M6 

58. Vibration Tests of jModified Kollsman Altimeter for Toss- 

Bombing Equipment, B. L. Wilson and Arnold Wexler, 
R(‘I)ort OD-SP-79, NBS, Ordnance Development Divi¬ 
sion, Jan. 17, 1945. Div. 4-322.1-M2 

59. Horizontal Range Errors Resulting from Altitude Ratio 

Errors, ,\rnold Wexler and Albert London, Report OD- 
SP-80, NBS, Ordnance Development Division, Jan. 18, 
1945. Div. 4-312.3-Ml 

60. Bomb Director Performance, Patuxent River Station, 

December 29, 1944 to January 31, 1945, .John II. Park, 
Report OD-SP-82, NBS, Ordnance Development Divi¬ 
sion, F>b. 16, 1945. Div. 4-321.3-Ml 

61. Minimum-Segment K-Block Design, Albert London and 
Ray F^. Smith, Jr., Report OD-SP-83, NBS, Ordnance 
Development Division, Feb. 9, 1945. Div. 4-236-MlO 

62. Grid Current in the 2050 Thyratron Tube, Harold N. 

Cones, R. W. Gustafson, and Robert L. Nutter, Report 
OD-SP-84, NBS, Ordnance Development Division, 
Feb. 8, 194.5. Div. 4-231.1-MlO 

63. Laboratory Tests of an Altitude-Switch for Use with 7'oss- 

Bombing Equipment, Arnold Wexler, B. L. \5'ilson, and 
F. O. Harrer, Report OD-SP-85, NBS, Ordnance Devel¬ 
opment Division, F’eb. 16, 1945. Div. 4-322.42-Ml 

64. Flight 7'ests of Iowa Integrator Mounted on A-l-A and 
New Design Shock Mount, Leroy R. Sweetman, Report 
OD-SP-86, NBS, Ordnance Development Division, FAb. 

8, 1945. Div. 4-324.3-M4 

65. Description of Test Unit Mk 16 Mod 0, V. W. Cohen, 

Report OD-SP-87, NBS, Ordnance Development Divi¬ 
sion, Mar. 1, 1945. Div. 4-321.4-Ml 


66. Rocket-Tossing Theory, Albert London and C. F. Eve, 

Report OD-SP-90, NBS, Ordnance Development Divi¬ 
sion, Feb. 24, 1945. Div. 4-421-M2 

67. Bench Tests on Magnavox Computers, R. W. Gustafson, 

Report OD-SP-91, NBS, Ordnance Development Divi¬ 
sion, Feb. 24, 1945. Div. 4-324.14-Ml 

68. Bomb Director Performance, Patuxent River Station, Febru¬ 

ary 1, 1945 to February 28, 1945, .John FI. Park, Report 
OD-SP-93, NBS, Ordnance Development Division, 
Mar. 10, 1945. Div. 4-321.3-Ml 

69. Tests on 2050 Thyratrons in Magnavox and NBS Test 

Units; Effectiveness of Heat Curing the Thyratrons, Harold 
N. Cones, Report OD-SP-95, NBS, Ordnance Develop¬ 
ment Division, Apr. 16, 1945. Div. 4-231.11-M2 

70. Humidity Tests on Production AN/ASG-10 and Various 

Cables, J. L. Pike and Joseph Johansen, Report OD-SP- 
96, NBS, Ordnance Development Division, Mar. 12, 
1945. Div. 4-321.11-Ml 

Addendum; Further Humidity Tests on AN/ASG-10 
Computer, Cables, Connectors, and Altimeter, J. L. Pike 
and Joseph Johansen, Report OD-SP-96A, Apr. 13, 1945. 

Div. 4-321.11-M3 

Second Addendum: Humidity Tests on AN/ASG-10 
Computer, Pilot’s Control Box, Altimeter, and Sealed 
Chamber Terminals, Report OD-SP-96B, J. L. Pike and 
Joseph Johansen, May 14, 1945. Div. 4-321.11-M5 

71. Wind Correction for I’oss Bombing, T. H. Nicholl, Report 

OD-SP-97, NBS, Ordnance Development Division, 
Mar. 14, 1945. Div. 4-312.4-M2 

72. Exact Solution of Toss Bombing Equations for Circular 

Pull-up, S. H. Lachenbruch, Albert London, and C. F. 
Eve, Report OD-SP-98, NBS, Ordnance Development 
Division, Mar. 23, 1945. Div. 4-311.1-M5 

73. Laboratory Tests of Electrical Altimeter A o. 2 for Use with 

Toss Bombing Equipment, Arnold Wexler and Ray F. 
Smith, Jr., Report OD-S P-99, NBS, Ordnance Develop¬ 
ment Division, Mar. 24, 1945. Div. 4-322.2-M3 

74. Summary of Time in Air for all Toss Bombing Equipment 

at Patuxent from 28 October 1944 to 19 March 1945, List¬ 
ing All Faults in Equipment and Adjustments Made, John 
H. Park, Report OD-SP-100, NBS, Ordnance Develop¬ 
ment Division, Mar. 27, 1945. Div. 4-321.11-M2 

75. Rocket and Bomb Tossing Circuit for Use with Photo¬ 

electric Accelerometer, William B. McLean, Preliminary 
Report OD-SP-101, NBS, Ordnance Development Divi¬ 
sion, Apr. 3, 1945. Div. 4-326.1-Ml 

76. Bomb Director Performance, Naval Air Station, Patuxent 

River, Md., March 1-31, 1945, W. Q. Hull, Report OD- 
SP-102, NBS, Ordnance Development Division, Apr. 10, 
1945. Div. 4-321.3-Ml 

77. First Button Releases in SB2C Planes, Their Cause and 
Probable Cure, John H. Park, Report OD-SP-103, NBS, 
Ordnance Development Division, Apr. 11, 1945. 

Div. 4-328.5-M2 

78. Angle of Attack of Thrust Line, Plane SB2C-4 Ser. 
20354 , John H. Park, Report OD-SP-104, NBS, Ord¬ 
nance Development Division, Apr. 14, 1945. 

Div. 4-311.4-M2 








186 


BIBLIOGRAPHY 


79. Range Limitations Resulting from Approximations in Toss 

Bombing Equations, S. H. Laclienbruph, Report OD-SP- 
105, NBS, Ordnance Development Division, Apr. 16, 
1945. Div. 4-314-Ml 

80. ILmd Correction Sighting Grids for Toss Bombing, .Albert 
London and .A. E. Willgoos, Report OD-SP-106, XBS, 
Ordnance Development Division, Alay 11, 1945. 

Div. 4-312.4-AI3 

81. Range Wind Correction for Toss Bombing, Albert London 
and C. F. Eve, Report OD-SP-107, NBS, Ordnance De¬ 
velopment Divdsion, .June 5, 1945. Div. 4-312.4-AI4 

82. Maintenance Xotes on AN/ASG-10 (XN) Equipment, 
F. M. Defandorf, Report OD-SP-109, NBS, Ordnance 
Development Division, Alay 1, 1945. Div. 4-321.11-AI4 

83. Protek (Silica Gel) Dryer Plugs Used in Computer for 
AX/ASG-10, Harold N. Cones, Report OD-SP-111, 
NBS, Ordnance Development Division, May 2, 1946. 

Div. 4-324.15-AIl 

84. Angle of Attack of Thrust Line, Plane F6F, 77555, L. .1. 

Jelsch, Report OD-SP-112, NBS, Ordnance Develop¬ 
ment Division, May 7, 1945. Div. 4-311.4-M3 

85. Bomb Director Performance Naval Air Station, Patuxent 

River, Md., April 1-30, 1945, John 11. Park, Report 
OD-SP-113, NBS, Ordnance Development Division, 
May 8, 1945. Div. 4-321.3-Ml 

86. Construction on Dive Angle Indicators (Gyro Repeaters) 

for Use with AX/ASG-10 Gear, .A. E. Peterson, Report 
OD-SP-116, NBS, Ordnance Development Division, 
May 21, 1945. Div. 4-327-M4 

87. Dependence of Range on the Alloicable Sight Depression in 
Dive Bombing, S. H. Lachenbruch, Report OD-SP-117, 
NBS, Ordnance Development Division, Alay 11, 1945. 

Div. 4-311.2-Ml 

88. Bomb Director Performance Naval Air Station, Patuxent 

River, Md., May 1-31, 1945, John H. Park, Report OD- 
SP-118, NBS, Ordnance Development Division, June 14, 
1945. Div. 4-321.3-AIl 

89. Toss Director using Photoelectric Accelerometer, Continuous 
Take-off Altimeter, and a Linear Condenser Charging Cir¬ 
cuit, William B. McLean, Report OD-SP-119, NBS, 
Ordnance Development Division, June 22, 1945. 

Div. 4-326.1-M2 

90. Thyratron Tube Tester, X. W. Cohen, Report OD-SP-120, 

NBS, Ordnance Development Division, June 23, 1945; 
Addendum, July 10, 1945. Div. 4-231.11-AI3 

91. Vibration Tests of Magnavox Computers, C. Weaver 
Creed and J. L. Pike, Report OD-SP-121, NBS, Ord¬ 
nance Development Division, July 24, 1945. 

Div. 4-324.3-M7 

92. Test Unit Mk 17 for Thyratron Tests, X. W. Cohen. Re¬ 

port OD-SP-122, NBS, Ordnance Development Division, 
July 9, 1945. Div. 4-231.11-M4 

93. ^ Function for Non-Constant Pull-up Acceleration, C. F. 
Eve and Albert London, Report OD-SP-123, NBS, Ord¬ 
nance Development Division, July 10, 1945. 

Div. 4-311.1-M7 

94. Angle of Attack of Bore-Sight Datum Line for SB2C-5, 

F 4 U, and F6F-5 Airplanes, John H. Park, Report OD- 
SP-124, NBS, Ordnance Development Division, June 22, 
1945. Div. 4-311.4-M4 


95. Gyroscope Turn Error Compensation, Forest K. Harris 
and Frank E. Inman, Report OD-SP-125, NBS, Ord¬ 
nance Development Division, July 11, 1945. 

Div. 4-325-M5 

96. Resume of AIBR Project in ETO Covering Period July 1, 

1944 lo June 6, 1945, William L. Whitson, Report OD- 
SP-126, NBS, Ordnance Development Division, July 12, 
1945. Div. 4-221-Ml 

97. Bomb Director Performance, Naved Air Station, Patuxent 

River, Md., June 1-30, 1945, John H. Park, Report 
OD-SP-127, NBS, Ordnance Development Division, 
July 12, 1945. Div. 4-321.3-Ml 

98. A Photoelectric Altimeter for Use with Toss Bombing 

Equipment, Arnold Wexler, Harold N. Cones, and Fred 
Nemir, Report OD-SP-128, NBS, Ordnance Develop¬ 
ment Division, Aug. 7, 1945. Div. 4-322.3-Ml 

99. Installation of Toss Bombing Equipment in an F7F-1 
Airplane, J. L. Pike, Report OD-SP-129, NBS, Ord¬ 
nance Development Division, July 27, 1945. 

Div. 4-340-M3 

100. Altimeter Shock Mounts, Arnold Wexler, Report OD- 

SP-130, NBS, Ordnance Development Division, July 23, 
1945. Div. 4-322.1-M3 

101. The Effect of Sight Misalignment and Angle of Attack 

Variation, S. H. Lachenbruch, Report OD-SP-131, 
NBS, Ordnance Development Division, July 23, 1945. 

Div. 4-312.1-M3 

102. Tests of Pitch Indicating Gyro with Added Freedom, about 
the Roll Axis, Frank E. Inman, Report OD-SP-132, 
NBS, Ordnance Development Division, July 25, 1945. 

Div. 4-325.1-M6 

103. An Improved Altimeter Unit Circuit for AX/ASG-10, 

J. L. Pike, Report OD-SP-133, NBS, Ordnance Develop¬ 
ment Division, Aug. 1, 1945. Div. 4-322.1-M4 

104. Flight Test of Conn Pitch-Indicating Gyro with Added 

Freedom about the Roll Axis, Forest K. Harris, Report 
OD-SP-134, NBS, Ordnance Development Division, 
Aug. 11, 1945. Div. 4-325.1-M7 

105. Wind Compensation of the Photoelectric Accelerometer 

when Used with a Lead-Computing Sight, Albert London, 
Rej)ort OD-SP-135, NBS, Ordnance Development Divi¬ 
sion, Aug. 21, 1945. Div. 4-326.1-M4 

106. Rack Lag Time for Mk 50 and Mk 45 Mod 1 Racks with 
AN/ASG-10 Gear, A. E. Peter.son, Report OD-SP-136, 
NBS, Ordnance Development Division, Aug. 23, 1945. 

Div. 4-317-Ml 

107. Distructions for Test of Bomb Director Mk 1 Mod 1, Prior 
to Installation, X. W. Cohen, Report OD-SP-137, NBS, 
Ordnance Development Division, Aug. 25, 1945. 

Div. 4-321.4-M2 

108. Photoelectric Accelerometer to Replace Gyro in Mk 1 

Mod 1 and 2 Bomb Directors, William B. AIcLean, Re¬ 
port OD-SP-138, NBS, Ordnance Development Divi¬ 
sion, .Aug. 12, 1945. Div. 4-326.1-M3 

109. Construction and Method of Operation of the Apparatus 

and its Component Elements (Translation from German 
of Paper by Zeiss on TAS), F. B. Silsbee, Report OD-SP- 
140, NBS, Ordnance Development Division, .Aug. 31, 
1945. Div. 4-321.4-M3 




BIBLIOGRAPHY 


187 


110. Portable DC Operated Test Unit, V. W. Cohen, Report 

OD-SP-141, NBS, Orilnance Development Division, 
Sept. 4, 1945. Div. 4-321.4-M4 

111. Calibration of Two Altimetric Slides, Arnold Wexler, and 
Robert L. Nutter, Report OD-SP-142, NBS, Ordnance 
Development Division, Sept. 6,1945. Div. 4-322.3-M2 

112. Instructions for the Modification of Gyro Unit Mk 20 
Mod 1, Frank E. Inman, Report OD-SP-144, NBS, 
Ordnance Development Division, Oct. 4, 1945. 

Div. 4-325-M7 

113. Analysis of Resistor Values Needed for Mk 3 Circuit, 

Martha C'ox, Ray F. Smith, Jr., and A. E. Willgoos, 
Report OD-SP-145, NBS, Ordnance Development 
Division, Sept. 20, 1945. Div. 4-328.2-M3 

114. Tactical Limitations of the Modified Altimeter Circuit, 

Albert London and S. H. Lachenbruch, Report OD-SP- 
146, NBS, Ordnance Development Division, Oct. 2, 
1945. Div. 4-322.42-M2 

115. Short Description of the Technique of Dynamic Testing of 

Aneroid Altimeters and Barometers, Arnold Wexler, 
Report OD-SP-147, NBS, Ordnance Development Divi¬ 
sion , Oct. 11, 1945. Div. 4-322.3-M3 

116. .4n Analytical Method for Correcting Systematic Toss 
Bombing Errors, Involving Revision of the ijc Function, 
S. H. Lachenbruch, Report OD-SP-150, NBS, Ordnance 
Development Division, Nov. 30, 1945. 

Div. 4-312.2-M7 

117. The Modified Linderman Dive Angle Indicator, McKay 
R. Bradley and F. L. Hermach, Report OD-SP-151, 
NBS, Ordnance Development Division, Dec. 31, 1945. 

Div. 4-327-M5 

118. Effect of Variation in Dive Angle and Release Altitude on 
Operation of Mk 1 Mod 1 Bomb Director in an SB2C-4 
Airplane, E. U. Rotor, Report OD-SP-152, NBS, Ord¬ 
nance Development Division, Jan. 10, 1946. 

Div. 4-321.2-M4 

119. Relay Lag Timing Errors in the Mk 20 Mod 2 Computer, 
F. R. Kotter, Report OD-SP-153, NBS, Ordnance 
Development Division, Jan. 31, 1946. 

Div. 4-324.14-M2 

120. Toss Bombing Trajectories, F. L. Celauro and D. Fisher, 

Memorandum OD-OAG-32, NBS, Ordnance Develop¬ 
ment Division, Sept. 6, 1944. Div. 4-313-Ml 

121. Field Tests with Toss Bombing Equipment Adjusted for 

Tossing Torpedoes, July 4 to September 9, 1944, ot 
Patuxent, Md., F. R. Kotter, Memorandum OD-SP- 
24M, NBS, Ordnance Development Division, Sept. 29, 
1944. Div. 4-340-Ml 

122. Sight Line Adjusted Off Line of Flight, William L. Whit¬ 

son, Memorandum OD-SP-43M, NBS, Ordnance Devel¬ 
opment Division, Nov. 11, 1944. Div. 4-323.2-M2 

123. Sight Settings, P. V. Johnson, Memorandum OD-SP- 

44M, NBS, Ordnance Development Division, Nov. 13, 

1944. Div. 4-323.2-M3 

124. Method of Checking the Alignment of the Sight with the 

Flight Line in a Dive, William B. McLean, Memorandum 
OD-SP-47M, NBS, Ordnance Development Division, 
Nov. 16, 1944. Div. 4-312.1-M2 


125. Alternative Integrator Circuit, F. B. Silsbee, Memoran¬ 

dum OD-SP-58M, NBS, Ordnance Development Divi¬ 
sion, Dec. 2, 1944. Div. 4-324.21-Ml 

126. Flight Curves for Patuxent Planes, F. R. Kotter, Memo¬ 

randum OD-SP-61M, NBS, Ordnance Development 
Division, Nov. 25, 1944. Div. 4-318-Ml 

127. Solenoid Operating Air Valve for Use with Dive Angle 
Indicator, F. M. Defandorf, Memorandum OD-SP-62M, 
NBS, Ordnance Development Division, Dec. 8, 1944. 

Div. 4-327-Ml 

128. Results of Field Test of Electrical Indicating Altimeter, 
Joseph H. Hibbs, Memorandum OD-SP-64M, NBS, 
Ordnance Development Division, Dec. 14, 1944. 

Div. 4-322.2-Ml 

129. Change of Shape of Gyro Card for Magnavox Production, 
William B. McLean, Memorandum OD-SP-67M, NBS, 
Ordnance Development Division, Dec. 26, 1944. 

Div. 4-325-M2 

130. Difference between Bomb Directors Mk 1 Mod 0 and Mk 1 
Mod t, F. B. Silsbee, Memorandum OD-SP-73M, NBS, 
Ordnance Development Division, Jan. 9, 1945. 

Div. 4-321.2-M2 

131. Angle of Attack of the Bore-Sight Datum Line in the 
F6F-5, Robert E. Holland, Memorandum OD-SP-74M, 
NBS, Ordnance Development Division, Jan. 1, 1945. 

Div. 4-311.4-Ml 

132. Sight Setting for TBM-lC as Determined with the Aid of 
a Theodolite on Dec. 6, 1944 o.t Patuxent, Md., Albert G. 
Hoyem, Memorandum OD-SP-75M, NBS, Ordnance 
Development Division, Jan. 1, 1945. Div. 4-323.2-M4 

133. Specifications of a Humidity Test Chamber, V. W. Cohen, 

Memorandum OD-SP-81M, NBS, Ordnance Develop¬ 
ment Division, .Jan. 24, 1945. Div. 4-619-M3 

134. Cycling Test of Raymond Modified Altimeter with New 

Whisker Design, Arnold Wexler, Memorandum OD-SP- 
84M, NBS, Ordnance Development Division, Jan. 31, 
1945. Div. 4-322.41-Ml 

135. Conversion of Jack and Heintz Horizon to Dive Angle 
Indicator, Forest K. Harris, Memorandum OD-SP-85M, 
NBS, Ordnance Development Division, Feb. 12, 1945. 

Div. 4-327-M3 

136. Report of Visit to MIT, February 16, 1945, [The K-11, 
or Mark 21 Sight as an Aid to Toss Bombing] William B. 
McLean, Memorandum OD-SP-87M, NBS, Ordnance 
Development Division, Feb. 23, 1945. 

Div. 4-323.1-M2 

136a. Recommendations on Gyro Processing at Magnavox on 
Basis of Visit to Ft. Wayne during Week of April 2, 1945, 
Frank E. Inman, Memorandum OD-SP-104M, NBS, 
Ordnance Development Division, Apr. 16, 1945. 

Div. 4-325-M3 

137. Trip to Eglin Field, March 3-8, 1945, William B. Mc¬ 
Lean, Memorandum OD-8-92M, NBS, Ordnance 
Development Division, Mar. 16, 1945. 

Div. 4-323.1-M3 

137a. Report on Visit to Groves, Sickle, and Sperry Plants, 
June 4-T, 1945 , Frank E. Inman, Memorandum OD-SP- 
114M, NBS, Ordnance Development Division, June 15, 
1945. Div. 4-325-M4 


istricteD ? 






188 


BIBLIOGRAPHY 


137b. Report on Magnavox Gyro Test Fixtures and Procedures, 
Forest K. Harris, Memorandum OD-SP-116M, NBS, 
Ordnance Development Division, .June 27, 1945. 

Div. 4-325.1-M5 

138. Bomb Director Mk 1 Mod 1 Specifications, F. B. Silsbee, 

Memorandum OD-SP-112M, NBS, Ordnance Develop¬ 
ment Division, June 11,1945. Div. 4-321.2-M3 

139. Altimeter Contacts, F. M. Defandorf, Memorandum 

OD-SP-119M, NBS, Ordnance Development Division, 
July 11, 1945. Div. 4-322.41-M2 

Addendum; Variations in Overhang of Altimeter Whisker, 
Aug. 13, 1945. Div. 4-322.41-M3 

140. Tables of MPI Settings Required for Different Bomb 

Ballistic Coefficients, C. F. Eve, Memorandum OD-SP- 
123M, NBS, Ordnance Development Division, July 20, 
1945. Div. 4-242.14-M3 

141. Tests of the Linderman Accelerometer, V. W. Cohen, 

Memorandum OD-SP-124M, NBS, Ordnance Develop¬ 
ment Division, July 30, 1945. Div. 4-326.2-Ml 

142. A List of Unsatisfactory Features in Mod 1 and 2 Equip¬ 

ment and Some Remedies, F. M. Defandorf, Memoian- 
dum OD-SP-126M, NBS, Ordnance Development Divi¬ 
sion, Aug. 14, 1945. Div. 4-321.11-M6 

143. Comments on Report on 2050 Tubes by G. E. Johnson to 

Lt. Bolser, July 20, 1945, V. W. Cohen, Memorandum 
OD-SP-130M, NBS, Ordnance Development Division, 
.\ug. 27, 1945. Div. 4-231.1-M12 

144. Stick Offset Setting Xomograph, C. F. Eve, Memorandum 

OD-SI’-133M, NBS, Ordnance Development Division, 
Aug. 30, 1945. Div. 4-328.1-M2 

145. Modification of Gyros with CAG-93, Frank E. Inman, 

Memorandum OD-SP-135]\I, NBS, Ordnance Develop¬ 
ment Division, Sept. 17, 1945. Div. 4-32.5-M6 

146. Change in Drag Tolerances of Altimeter Unit, .\rnold 
Wexler, Memorandum OD-SP-136M, NBS, Ordnance 
Development Division, Oct. 11, 1945. 

Div. 4-322.5-M2 

146a. K-Bob Springs, Arnold Wexler, Memorandum OD-SP- 
141M, NBS, Ordnance Development Division, Nov. 1, 
1945. Div. 4-324.22-M4 

147. Tables of Operational Limits in Toss Bombing, C. F. 
Eve, Memorandum OD-SP-140M, NBS, Ordnance 
Development Division, Oct. 29, 1945. 

Div. 4-314-M2 

148. Elimination of Gyro-Turn Error, and Automatic Caging 
of Gyro, Frank E. Inman, Memorandum OD-SP-142M, 
NBS, Ordnance Development Division, Nov. 8, 1945. 

Div. 4-325-M8 

149. The Electrically Driven Attitude Gyro, Frank E. Inman, 

Memorandum OD-SP-144M, NBS, Ordnance D('velop- 
ment Division, Nov. 26, 1945. Div. 4-325-M9 

150. Progress Reports of Special Group on Toss Bombing, 

July 24, 1944 io January 31, 1946, W. S. Hinman, Jr., 
and William B. McLean, NBS, Ordnance Development 
Division, NDRC-4. Div. 4-311-M5 


NDRC DIVISION 4 CONTRACTORS’ REPORTS 
State University of Iowa 

151. Mathematical Study of Toss Bombing in the General Casey 
Irvin H. Swift, OEMsr-769, Interim Report 7, State 
University of Iowa, May 22, 1943. Div. 4-311-M2 

152. Preliminary Discussion on Electronic Timer, REI-1,. 
State University of Iowa, Dec. 1, 1943. 

153. Excerpts from University of Iowa Report Concerning the 
Theory of Toss Bombing, OEMsr-769, Report A-S117BT, 
State University of Iowa, Aug. 5, 1944. Div. 4-311-M6 

154. .4 Discussion of Toss Bombing Data Taken at Wright 
Field, Robert E. Holland, OEMsr-769, Technical Paper 
A-S120 ERDS, State University of Iowa, Aug. 11, 1944. 

Div. 4-311-M7 

155. Checking and Adjusting Procedure for Clare A-16494 

Relays, OEMsr-769, Report A-S138A, State University 
of Iowa, Oct. 17, 1944. Div. 4-328.41-Ml 

156. The Elements of Toss Bombing, Irvin H. Swift, OEMsr- 

769, Technical Paper REI-TMD-115, Rev. 1, State 
University of Iowa, Nov. 4, 1944. Div. 4-311-M9 

157. Test Program on Rocket Tossing at Patuxent, Irvin H. 

Swift, and James A. Jacobs, Report A-S-146 EP, State 
Univereity of Iowa, Nov. 4, 1944. Div. 4-423-Ml 

158. Leakage Effect with Combination Integrator and PCB 
Irvin H. Swift, OEMsr-769, Memorandum MC-1-1-45 
State University of Iowa, Revised: Mar. 31, 1945. 

Div. 4-324.3-M6 

159. .4h Upper Limit for Angular Mil Separation in Range 

between Two Rockets Launched Simultaneously, Carl E. 
Noble, OEMsr-769, Report MC-1-2-45, State LTniver- 
sity of Iowa, Jan. 6, 1945. Div. 4-412.4-M5 

160. Rocket Tossing — Results of SP-5 Tests with the TBM-lC 

at Patuxent, Albert C. Hoyem, OEMsr-769, Memoran¬ 
dum MC-1-3-45, State University of Iowa, Jan. 13, 
1945. Div. 4-421.2-Ml 

161. The Effect of Certain Modifications in the Integrator 
Circuit, Irvin H. Swift, OEMsr-769, Memorandum 
MC-2-1-45, State University of Iowa, Feb. 17, 1945. 

Div. 4-324.21-M3 

162. The Method of Reducing Aircraft Data Used by the Uni¬ 

versity of Iowa Rocket Tossing Group at the Naval Ord¬ 
nance Test Station, Inyokern, California, Carl E. Noble, 
OEMsr-769, Memorandum MC-2-2-45, State Univer¬ 
sity of Iowa, Feb. 17, 1945. Div. 4-421.2-M2 

163. Results of Tests on Switches of the Micro Switch Type, 
T. C. Stephens, OEMsr-769, Memorandum MC-2-3-45, 
State University of Iowa, Feb. 24, 1945. 

Div. 4-324.22-M3 

164. Pull-up Acceleration as a Function of Time for F6F and 

TBM Flights Releasing Rockets and Bombs, A. H. Crip- 
pen, OEMsr-769, Memorandum MC-2-4-45, State Uni¬ 
versity of Iowa, Feb. 24, 1945. Div. 4-316-Ml 

165. Theodolite Measurement of Sight Setting for SB2C-4 No, 
19717, A. H. Crippen, OEMsr-769, Memorandum 
MC-3-1-45, State University of Iowa, Mar. 10, 1945. 

Div. 4-323.2-M.5 





BIBLIOGRAPHY 


189 


166. The Ejfect of Plane Velocity on MPI in Tossing Rockets 

at Patuxent, Robert E. Holland, OEMsr-769, Memo¬ 
randum MC-4-1-45, State University of Iowa, Apr. 14, 
1945. Div. 4-421.2-M3 

167. Shift in MPI with Change in A Factor in Rocket Tossing, 
Irvin H. Swift, OEM.sr-769, Memorandum MC-4-2-45, 
State University of Iowa, Apr. 28, 1945. 

Div. 4-421.2-M4 

168. Sight Settings for Tossing Compared xcith CIT Attack 
Angle Values, T. C. Stephens, OEMsr-769, Alemoran- 
dum M7-5-1-45, State University of Iowa, May 5, 1945. 

Div. 4-422.1-M4 

169. Empirical Equation for the Trajectory Drop of Present 

Model 11.75" Aircraft Rocket, M. E. Rolfs, OEMsr-769, 
Memorandum M7-6-1-45, State University of Iowa, 
June 6, 1945. Div. 4-412.1-M9 

170. Revision of Empirical Equation for Trajectory Drop of 
5.0"AR, M. E. Rolfs, OEMsr-769, Memorandum 
M7-6-2-45, State University of Iowa, June 6, 1945. 

Div. 4-412.1-MlO 

171. Note Concerning the Function F (a), L. E. Ward, 

OEMsr-769, Memorandum M7-6-3-45, State University 
of Iowa, June 13, 1945. Div. 4-412.1-Mll 

172. An Empirical Equation for Trajectory Drops of 3.5" 

Aircraft Rocket, M. E. Rolfs, OEMsr-769, Technical 
Paper TC-1-1-45, State University of Iowa, Revised; 
Jan. 20, 1945. Div. 4-412.1-M5 

173. The Motion of Aircraft Rockets During Burning, L. E. 
Ward, OEMsr-769, Technical Paper TC-1-2-45, State 
University of Iowa, Jan. 13, 1945. Div. 4-412.2-M4 

174. Empirical Equations for Trajectory Drops of 11.75" Air¬ 
craft Rocket and 5.0" High Velocity Aircraft Rocket, 
M. E. Rolfs, OEM.sr-769, Technical Paper TC-1-3-45, 
State Univensity of Iowa, Jan. 27, 1945. 

Div. 4-412.1-M6 

175. Effect of a Constant Angle between the Sight Line and the 

Flight Line in Tossing Projectiles, M. E. Rolfs, OEMsr- 
769, Technical Paper TC-2-1-45, State LTniversity of 
Iowa, Feb. 24, 1945. Div. 4-311.1-M4 

176. An Equation for the Rocket Tossing Pull-Up Time Tp, 
L. E. Ward, OEMsr-769, Technical Paper TC-2-2-45, 
State University of Iowa, Feb. 24, 1945. 

Div. 4-421.1-Ml 

177. Empirical Equations for Trajectory Drops of 2.25" AR 
(fast), RP-S, 3.5", 5.0" AR, and RP-3, 5.0", M. E. 
Rolfs, OEMsr-769, Technical Paper TC-3-1-45, State 
Univer.sity of Iowa, Mar. 31, 1945. Div. 4-412.1-M7 

178. The Results Obtained from Firing 5.0" HVAR with the 
Toss Sight in an F6F-5 cd Inyokern, Carl E. Noble, 
OEMsr-769, Technical Paper TC-4-1-45, State Univer¬ 
sity of Iowa, Revised: July 18, 1945. Div. 4-422.1-M6 

179. Values of the A Factor for Rocket Tossing, Irvin H. 
Swift, OEMsr-769, Technical Paper TC-4-2-45, State 
University of Iowa, Apr. 7, 1945. Div. 4-421.1-M2 

180. An Equation for the Rocket Tossing Pull-Up Time Tp, 

when Spatial Acceleration Varies with Time, L. E. Ward, 
OEMsr-769, Technical Paper TC-4-3-45, State Uni¬ 
versity of Iowa, Apr. 7, 1945. Div. 4-421.1-M3 


181. Summary of Data of Tossing 3.5" AR’s Obtained with 

TBM-lC 45^73 at Patuxent, .Albert G. Iloyem, OEMsr- 
769, Technical Paper TC-4-4-45, State University of 
Iowa, .Apr. 14, 1945. Div. 4-422.1-M2 

182. IFiVu/ Corrections for the Toss Sight in Forward Firing of 

Rockets from Aircraft, M. E. Rolfs, OE.Msr-769, Tech¬ 
nical Paper TC-4-5-45, State LIniver-sity of Iowa, .Apr. 
21,1945. Div. 4-422.1-M3 

183. Pull-Up Angle at Start of Integration, Phillip G. Hub- 
hard, OEMsr-769, Technical Report TC-4-6-45, State 
University of Iowa, Revised: July 4, 1945. 

Div. 4-311.1-M6 

184. Actual Operation of an REIX Combination Unit when 

Spatial Acceleration Varies with Time, Phillip G. Hub¬ 
bard, OEMsr-769, Technical Paper T7-5-1-45, State 
University of Iowa, May 5, 1945. Div. 4-422.3-Ml 

185. The Effect of Change of Angle of Attack of an Airplane 

on Rocket Tossing Pull-Up Time, L. E. Ward, OEMsr- 
769, Technical Paper No. T7-5-2-45, State Univer.sity 
of Iowa, May 30, 1945. Div. 4-421.1-M4 

186. Operation of the AA'/ASG-IO Mk 1 Mod 2 Bomb Rocket 

Director for Rocket Tossing, Irvin H. Swift, OEMsr-769, 
Technical Report T7-6-1-45, State University of Iowa, 
June 13, 1945. Div. 4-422.2-Ml 

187. The Results Obtained from Launching 5.0" HVAR with 
the Toss Sight in an F 4 U-ID at Inyokern, Phillip G. 
Hubbard, OEMsr-769, Technical Report T7-6-2-45, 
State Univer.sity of Iowa, June 20, 1945. 

Div. 4-422.1-M5 

188. Summary Report on Rocket Tossing Theory, Irvin H. 

Swift, OEM.sr-769, Technical Report T7-7-2-45, State 
University of Iowa, July 25, 1945. Div. 4-421-M3 

189. General Summary of Rocket Tossing Field Tests, .Albert 
G. Hoyem, OEMsr-769, Technical Report T7-7-3-45, 
State University of Iowa, July 25, 1945. 

Div. 4-423-M2 

190. Iowa Experience with Vibration Tests on REIX-T 4 
Units, George S. Carson, OEMsr-769, Alemorandum 
M.A-11-1-44, State University of Iowa, Nov. 21, 1944. 

Div. 4-324.3-M2 

191. Preliminary Test Procedure for REIX-T 4 Revised for 

Circuit 326, George S. Carson, OEMsr-769, Memoran¬ 
dum MA-12-1-44, State University of Iowa, Revised; 
Feb. 10, 1945. Div. 4-324.3-M5 

192. Temperature Cycling Tests on Shallcross Resistors, 
George S. Carson, OEMsr-769, Memorandum MA-12- 
2-44, State University of Iowa, Revised; Jan. 27, 1945. 

Div. 4-236-M9 

193. Investigation of Thyratron 2050 Filament Voltage, John I. 
Gansert, OEMsr-769, Memorandum MA-1-1-45, State 
University of Iowa, Jan. 20, 1945. Div. 4-328.2-Ml 

194. Investigation of U-Block Vibration, A. H. A'oumans, 

OEMsr-769, Memorandum MA-1-2-45, State Univer¬ 
sity of Iowa, Jan. 20, 1945. Div. 4-238.6-Ml 

195. Integrator Test Procedure, Lloyd 0. Herwig, OEMsr-659, 

Memorandum M.A-1-3-45, State University of Iowa, 
Jan. 27, 1945. Div. 4-324.3-Ma 





190 


BIBLIOGRAPHY 


196. Supplementary Data on U-Block Vibration, A. H. Y'ou- 
mans and George S. Carson, OEMsr-769, Memorandum 
MA-2-2-45, State University of Iowa, Feb. 24, 1945. 

Div. 4-238.6-M2 

197. Summary Technical Report, Contract OEMsr-769, Chap. 

1, State University of Iowa, Sept. 29, 1945. 

Div. 4-100-M7 

198. Progress Reports, State University of Iowa, NDRC-4. 

The Magnovox Company 

199. Type Test of AN/ASG-10, Serial 1004 and 1555 July 6 
to August 13, 1945 , Magnavox Company. 

Div. 4-321.1-M3 

200. Quality Control Report for Bomb Director Test Equipment 

Mk 17 Mod 0, TS-362/ASG-10, Serial 204 and 212, C. B. 
Fine and W. Harl, Magnavox Company, Sept. 25 and 
Sept. 26, 1945. Div. 4-321.4-M5 

201. Type Test of AN/ASG-lOA November 26 to 29, 1945, 

C. B. Fine and \V. Harl, Magnavox Company, Novem¬ 
ber 1945. Div. 4-321.1-M4 

202. Report on AN/ASG-10 Bomb Director Development, 

Design, and Production (includes; Pilot’s Operating 
Manual for Bomb Director Mk 1 Mod 1, AN/ASG-10, 
Report CO-NAVAER 08-5S-501, January 17, 1945; 
Operator’s Manual for Bomb Director Mk 1 Mod 2, 
AAV A SG-1OA, Report CO-NAVAER 16-5S-524, June 15, 
1945; Handbook of Maintenance Instructions for Bomb 
Director Mk 1 Mod 1 AN/ASG-10, Report CO-AN 16-30 
ASCI0-7, August 1, 1945), R. II. Dreisbach and N. F. 
Alartin, OSRD Contract OEMsr-1417, Alagnavox 
Company, May 9, 1946. Div. 4-321.1-M5 

Raymond Engineering Laboratory, Inc. 

203. A Study of the Properties of Electrical Contact Resistance 

under Very Light Pressures and Under Light Electrical 
Load, Lloyd E. Stein [OEMsr-1378], Engineering Re¬ 
port 225, Raymond Engineering Laboratory, Inc., 
Jan. 6, 1945. Div. 4-750-Ml 

204. Test of ElectricGyroCaging Mechanism, H. H. Raymond, 

[OEMsr-1378], Report 230, Raymond Engineering Lab¬ 
oratory, Inc., Jan. 27, 1945. Div. 4-325.1-M3 

205. Test of X-2 Altimeter (A to D), T. H. Carter, [OEMsr- 
1378], Report 226, Raymond Engineering Laboratory, 
Inc., Jan. 18, 20, 26, and Feb. 2, 1945. Div. 4-322.5-Ml 

206. Tests of Electric Gyro Caging Mechanism with Electro- 

7 nagnetic Brake, K.G. BsLcheWor, [OEMsr-1378], Report 
232, Raymond Engineering Laboratory, Inc., Mar. 15, 
1945. Div. 4-325.1-M4 

207. Final Technical Report of Raymond Engineering Labora¬ 

tory, Inc., on Work Done under Contract OEMsr-1378, 
Report 238, Raymond Engineering Laboratory, Inc., 
Oct. 29, 1945. Div. 4-100-M8 

Bowen and Company 

208. Pilot Production of Toss Bombing Equipment, [OEMsr- 

1227], Electronics Division, Bowen and Company, Inc., 
May 1945. Div. 4-321.1-M2 


OTHER NDRC DIVISION REPORTS 
Applied Mathematics Group 

209. Toss Bombing with Target Motion, Harry Pollard, AMG 

Working Paper 293, Study 146, AMC-Columbia, Oct. 
24,1944 Div. 4-311-M8 

209a. The Transient of a Single Gyro Sight with Fixed Sensi¬ 
tivity, Harry Pollard, OEMsr-1007, AMG Working 
Paper 406, AMG-Columbia, Apr. 24, 1945. 

AMP-502.1-M22 

2091). The Failure of the Mark 18 as a Collision Course Deter¬ 
miner, Harry Pollard, AMG Report 371, AMG-Colurn- 
bia, Feb. 20, 1945. Div. 4-422.1-Ml 

210. A Particular Method of Aiming Bombs and Rockets, 
Hassler Whitney, OEMsr-1007, AMG Report 335, 
Study 124, AMG-Columbia, Dec. 15, 1944. 

AMP-601. 2-M4 

210a. An Introduction to the Analytical Principles of Lead 
Computing Sights, Saunders MacLane, NDRC, AMP 
Memo 55.1, Mar. 27, 1944. Div. 4-323.1-Ml 

211. A Solution of the Azimuth Problem in Toss Bombing, 
Harry Pollard, OEMsr-1007, AMG Working Paper 438, 
Study 146, AMG-Columbia, June 9, 1945. 

AMP-803.5-M9 

California Institute of Technology 

212. A Theory of Toss Bombing, Harry Pollard, OEMsr-1007, 

AMP Report 146-IR, AMG Working Paper 411, AMG- 
Columbia, September 1945. Div. 4-311-MlO 

213. Bore Sighting and Effective Angle of Attack Data for 
Various Aircraft, OEMsr-418, OSRD 2254, Service 
Projects OD-162, OD-164, and NO-170, Div. 3 Report 
CIT/UNC-2, CIT, Oct. 25, 1944. Div. 4-411.4-Ml 

214a. F4U-1, F 4 U-ID, FG- 1 : Sight Settings for 2.25", 3.5", 
and 5.0" Aircraft Rockets, OEMsr-418, OSRD-2271, 
Div. 3 Report CIT/UNC-4, CIT, Nov. 14, 1944. 

Div. 4-411.4-M2 

214b. F6F-3, F6F-5: Sight Settings for 2.25", 3.5", and 5.0" 
Aircraft Rockets, OEMsr-418, OSRD 2272, Service 
Projects OD-162, OD-164, and NO-170, Div. 3 Report 
CIT/UNC-5, CIT, Nov. 18, 1944. 

Div. 4-411.4-M3 

214c. TBM-1, TBF- 1 : Sight Settings for 2.25", 3 5", and 5.0" 
Aircraft Rockets, OEMsr-418, OSRD 2273, Div. 3 
Report CIT/UNC-6, CIT, Nov. 28, 1944. 

Div. 4-411.4-M5 

214d. TBM-IC, TBF-IC: Sight Settings for 2.25", 3.5", and 
5.0" Aircraft Rockets, OEMsr-418, OSRD 2274, Div. 3 
Report CIT/UNC-7. CIT, Dec. 1, 1944. 

Div. 4-411.4-M6 

214e. SB 2 C- 1 , SB 2 C- 1 C, SB2C-3, SB2C-4: Sight Settings for 
2.25", 3.5", and 5.0" Aircraft Rockets, OEMsr-418, 
OSRD 2275, Service Projects OD-162, OD-164, and 
NO-170, Div. 3 Report CIT/UNC-8, CIT, Nov. 23, 

Div. 4-411.4-M4 

215. Method of Compiding T rajectories and Sighting Tables for 
Forward Firing Aircraft Rockets, L. Blitzer and L. Davis, 
Jr., OEMsr-418, OSRD 3361, Service Projects NO-33 
and NO-170, Div. 3 Report CIT/JPC-17, CIT, Feb. 20, 
19-14. Div. 4-412.1-Ml 





BIBLIOGRAPHY 


191 


216. Trajectories of Aircraft Rockets: 3.5" and 5.0", OEMsr- 

418, OSRD 2225, Service Projects 014-162, OD-164, 
and NO-170, Div. 3 Report CIT/UBC-27, CIT, Sept. 
25, 1944. Div. 4-412.1-M2 

217. Trajectories of 11.75" Aircraft Rockets, OEMsr-418, 

OSRD 2290, Div. 3 Report CIT/UBC-30, CIT, Nov. 17, 
1944; Supplementary Data on Improved 11.75" Air¬ 
craft Rocket, May 1945. Div. 4-412.1-M3 

218. Trajectories of 5.0" High Velocity Aircraft Rocket and 
2.25" Practice Round, OEMsr-418, OSRD 2314, Div. 3 
Report CIT/UBC-32, CIT, Dec. 15, 1944. 

Div. 4-412.1-M4 

Radiation Laboratory, MIT 

219. Use of Radar Range for Toss Bombing, J. R. Rogers and 

J. \V. Gray, Div. 14 Report 63, [MIT, Radiation Labo¬ 
ratory], Apr. 21, 1943. Div. 4-315-Ml 

NAVY 

Bureau of Ordnance 

220. Bomb Director Mk 1 Mod 0 (AN/ASG-10 (XN) ), 
Description and Instructions for Use, Bur. of Ord. OP 
1306 (Preliminary), Apr. 6, 1945. 

221. Ordnance Specifications, Bomb Director Mk 1 Mod 1, 
Bureau of Ordnance, NAVORD OS 3606, June 23, 
1945 — Modifications: Letter Bu. Ord. (Pr2b), Aug. 7, 
1945; Letter Bu. Ord. (Pr2b) Oct. 1, 1945; Letter Bu. 
Ord. (Pr2b) Nov. 2, 1945. 

222. Ordnance Specifications, Bomb Director Mk 1 Mod 2i 
Bureau of Ordnance, NAVORD OS 3892, Nov. 13, 
1945 — Modifications: Letter Bu Ord (Pr2b) Nov. 13, 
1945; Letter Bu Ord (Pr2b) Jan. 7, 1946. 

Bureau of Aeronautics 

223. Installation Specification, Model AN/ASG-10 (XN-1) 
Airborne Bomb Director Equipment, Bureau of Aero¬ 
nautics, NAVAER-EI-144A, May 9, 1945. 

224. Installation Specification Model AN/ASG-10 Airborne 
Bomb Director Equipment, Bureau of Aeronautics, 
NAVAER-EI-153A, June 20, 1945. 

225. Installation Specification for Bomb Director Mk 1 Mod 2 
AN/ASG-lOA Airborne Installation, Bureau of Aero¬ 
nautics, NAVAER-EI-169, July 21, 1945. 

226. Descriptive and Performance Specifications for AN/ASG- 
10 (XN) Computing Set, Bureau of Aeronautics, 
NAVAER-EP-216A, Dec. 22, 1944. 

227 Descriptive and Performance Specifications for AN/ASG- 

10 Computing Set, Bureau of Aeronautics, NAVAER- 
EP-254, Jan 4, 1945 — Modification I, Feb. 12, 1945; 
Modification II, Apr. 21, 1945. 

228. Descriptive and Performance Specifications for AN/ASG- 
lOA Computing Set, Bureau of Aeronautics, NAVAER- 
EP-281, Mar. 5, 1945. 

229. Descriptive and Performance Specifications for AN / A SG- 
lOB Computing Set (Mk 3), Bureau of Aeronautics, 
NAVAER-EP-282A, June 27, 1945. 

230. Test Specification for Bomb Director Mk 1 Mod 0 
AN/ASG-10 (XN-1) Airborne Installation, Bureau of 
Aeronautics, NAVAER-ET-135, Mar. 31, 1945. 


231. Test Specification for Bomb Director Mk 1 Mod 1, 
AN/ASG-10 Airborne Installation, Bureau of Aero- 
nautic.s, N.\V.\ER-ET-137A, May 7, 1945. 

232. Test Specification for Bomb Director Mk 1 Mod 2, 
AN/ASG-lOA Airborne Installation, Bureau of Aero¬ 
nautics, NAVAER-ET-142, Aug. 13, 1945. 

232a. Pilot’s Operating Manual for Bomb Director Mk 1 
Mod 1, AN/ASG-10, Report CO-NA\^\ER 08-5S-501. 
Jan. 17, 1945. Div. 4-321.1-M5 

232b. Operator’s Manual for Bomb Director Mk 1 Mod 2, 
AN/ASG-lOA, Report CO-NAVAER 16-5S-524, June 
15, 1945. Div. 4-321.1-M5 

232c. Handbook of Maintenance Instructions for Bomb Director 
Mk 1 Mod 1, AN/ASG-10, Report CO-AN 16-30ASG10- 
7, .4ug. 1, 1945. Div. 4-321.1-M5 

Naval Research Laboratory 

233. Final Report on Type Test of AN/ASG-10 (XN) Equip¬ 
ment, Naval Research Lab., Report C-F42-5 (311-1: 
nVF-MLB), Serial No. C-310-28/45 (Ibr), Feb. 20, 
1945. 

234. Final Report on Tests of AN/ASG-10 Cable Insulation 
Resistance, Naval RevSearch Lab. Report C-F42-5/A62 
(311-1:FWB) Serial No. C-310-102/45 (rab). May 12, 
1945. 

235. Interim Report on Type Test of AN/ASG-10, I. W. Fuller 
and M. L. Burnett, Naval Research Laboratory R-2609, 
Aug. 2, 1945. 

236. Final Report on Type Test of TS-362/ASG-10, Naval 
Research Lab. Report C-F42-5 (311-1:I\VF:MLB), 
Serial No. C-310-186/45 (mec). Sept. 22, 1945. 

237. Excerpts from ACG Field Reports, Airborne Coordinat¬ 
ing Group, Naval Research Lab. 

Naval Ordnance Plant 

238. Toss Bomb Memoranda, Naval Ordnance Plant, Lukas- 
Harold Corp., September 1944-February 1945. 

238a. Gunsight Mark 23, Research Technical Report No. 18, 
Naval Ordnance Plant, Lukas-Harold Corp., Mar. 5, 
1945. 

Naval Air Station, Patuxent River 

239. Preliminary Report of Tests of Toss Bombing with Modi¬ 
fied AIBR Equipment and AYF Altimeter, Tactical Test, 
Naval Air Station, Patuxent River, Md., Project TED 
No. PTR-31A11, Mar. 22, 1944. 

240. Final Report on Evaluation of Toss Bombing Equipment, 
Tactical Test, Naval Air Station, Patuxent River, Md., 
Project TED No. PTR-31A11, Serial S-066, Jan. 19, 
1945. 

241. Preliminary Report on Comparison of the Tactical Test 
Toss Bombing Integrator with the Bureau of Standards 
Integrator and Report on Preliminary Flight Tests of the 
Tactical Test Integrator, Tactical Test, Naval Air Station, 
Patuxent River, Md., Project TED No. PTR-31A75, 
Serial S-070, Feb. 20, 1945. 

242 Requirements and Recommendations for A Sight to he 
Used with AN/ASG-10 Equipment. Tactical Test, Naval 
Air Station, Patuxent River, Md., Project TED No. 
PTR-31A75, Serial C-0106, Feb. 24, 1945. 




192 


BIBLIOGRAPHY 


243. Interim Report on Development of AN/ASG-10 (XN) and 
AN/ASG-10, Tactical Test, Naval Air Station, Patuxent 
River, Md., Project TED No. PTR-31A75, Serial 
C-0114, Apr. 10, 1945. 

244. Final Report on Test of I'oss Bombing Equipment in the 
F4U Airplane, Tacticcd Test, Naval Air Station, Patux¬ 
ent River, Md., Project TED No. PTR-31A52, Serial 
S-076, Apr. 27, 1945. 

245. Final Report on Tactical Evaluation of Computing Set 
AN/ASG-10 (XN) in SB2C-3, -4 Airplanes, Tactical 
Test, Naval Air Station, Patuxent River, Md., Project 
TED No. PTR-31A68, Serial S-081, IVIay 28, 1945. 

246. Interim Report on Tactical Evaluation of AN/ASG-10 at 
Safest Attacking Conditions, Tactical Test, Naval Air 
Station, Patuxent River, Md., Project TED No. 
PTR-31A91, Serial C-762, June 22, 1945. 

247. Interim Report on Tactical Evaluation of AN/ASG-10 at 
Safest Attacking Conditions in the F4U-4 Airplane, 
Tactical Test, Naval Air Station, Patuxent River, Md., 
Project TED No. PTR-31A91, Serial C-711, July 26, 
1945. 

248 Interim Report on Tactical Evaluation of AN/ASG-10 in 
the SB2C-5 Airplane at Attacking Conditions which will 
Afford a High Degree of Safety, Tactical Test, Naval Air 
Station, Patu.xent River, Md., Project TED No. PTR- 
31A91, Serial C-782, Sept. 13, 1945. 

249. Final Report on Tactical Evaluation of Rocket Tossing 
with Modified AN/ASG-10 (XN) Computing Set, Tacti¬ 
cal Test, Naval Air Station, Patuxent River, Md., 
Project TED No. PTR-31A70, Serial S-088, Sept. 26, 
1945. 

249a. Letter, Serial C-0105, Tactical Test, Naval Air Station, 
Patuxent River, Md., Feb. 20, 1945. 

250. Installation of AN/ASG-10{XN) in TBM-3 Airplane 
No. 22875, Radio Test, Naval Air Station, Patuxent 
River, Md., Project TED No. PTR-31733.0, Dec. 4, 
1944. 

251. Prototype Installation and Flight Test of AN/ASG-10 
(XN) Equipment in SB2C-4 Airplane, Radio Test, 
Naval Air Station, Patuxent River, Md., Project TED 
No. PTR-31723.0, Mar. 17, 1945. 

252. Flight Test of Prototype Installation of Bomb Director 
Mk 1 Mod 1 , AN/ASG-10 in TBM-3E Airplane No. 
69172, Radio Test, Naval Air Station, Patuxent River, 
Md., Project No. PTR-31803.1, Apr. 14, 1945. 

253. Flight Test of Bomb Director Mk 1 Mod 1, AN/ASG-10, 
in TBM-3E Airplane BuNo 85510, Radio Test, Naval 
Air Station, Patuxent River, Md., Project No. PTR- 
31803.2, May 7, 1945. 

254. Flight Test of Bomb Director Mk 1 Mod 1, AN/ASG-10 
in FG-l-D Airplane BuNo 76628, Radio Test, Naval Air 
Station, Patuxent River, Md., Project TED No. PTR- 
31818.0, May 12, 1945. 

Naval Air Station, Asdevlant, Quonset Pt. 

255. Toss Bombing at Low Altitude, Project 538, Asdevlant, 
Naval Air Station, Quonset Pt., R. I., letter ASDD/F41, 
Serial 00118, Oct. 6, 1944. 


255a. Toss Bombing Combined with Ballistic Aiming, Asdev¬ 
lant, Naval Air Station, Quonset Pt., R. L, Letter 
ASDD/F41, Serial 118, Oct. 16, 1944. 

256. Interim Report on Bomb (Rocket) Director JMk 1 Mod 0, 
Asdevlant Naval Air Station, Quonset Pt., R. I., 
Project 538, Serial 099, Mar. 1, 1945. 

257. Report on Bomb Director Mk 1 Mod 0 (AN/ASG-10)y 
Asdevlant, Naval Air Station, Quonset Pt., R. I., 
Project 538, Serial 0256, May 23, 1945. 

258. Report on Toss-Rockets (Bomb Director Mk 1 Mod 0, 
AN/ASG-IOXN), Asdevlant, Naval Air Station,. 
Quonset Pt., R. I., Project 538, Serial 0286, June 11, 
1945. 

259. Report on Simultaneous Tossing of Bombs and Rockets 
with Bomb Director Mk 1 Mod 0 (AN/ASG-IOXN)^ 
A.sdevlant, Naval Air Station, Quonset Pt., R. I., 
Project 538, Serial 0487, Sept. 20, 1945. 

Naval Ordnance Test Station, Inyokern, California 

259a. Interim Report on Test of Bomb Director Mark 1 Mod. 0, 
AN/ASG-10 for Rocket Fire Direction (F6F-5 Plane),. 
NOTS Project No. 23.3 AS. 

259b. Interim Report on Test of Bomb Director Mark 1 Mod. 0, 
AN/ASG-10 for Rocket Fire Direction (F 4 U-ID Plane),. 
NOTS Project No. 23.3 AS. 

ARMY 

Ordnance Department 

260. A Simplified Method of Sighting and Releasing Bombs 
from Airplanes, Lt. Col. H. S. Morton, Ordnance De¬ 
partment, Feb. 13, 1943. 

261. Preliminary Mathematical Analysis of Toss Bombing, 
Lt. Col. H. S. Morton, Ordnance Department, Feb. 13, 
1943. 

262. General Technique for Bombing Stationary or Moving 
Targets, Lt. Col. H. S. Morton, Ordnance Department, 
Feb. 22, 1943. 

263. Plane-to-Plane Bombing: IMathematical Study of the 
Timing Function of the Acceleration Integrator, Lt. Col. 
H. S. iMorton, Ordnance Dept., Feb. 25, 1943. 

264. Electriccd Integrator and Timer, Lt. Col. H. S. Morton, 
Ordnance Dept., June 16, 1944. 

AAF 

265. Preliminary Report on Test of Bombing Attack on Air¬ 
planes in Formation; Toss Bombing with Radar Range 
Phase, Proof Department, AAF Proving Ground Com¬ 
mand, Eglin Field, Fla., Serial No. 1-42-60, Aug. 19, 
1943. 

266. Air-to-Ground Toss Bombing Using Acceleration Inte¬ 
grator, AAF Center, Orlando, Fla. (AAF Proving 
Ground Command, Eglin PJeld, Fla.), AAF Board 
Project No. Q3648, Aug. 8, 1945. 

267. Fighter Bomber Accuracy Against Ground Targets, 
AAF Center, Orlando, Fla. (AAF Proving Ground Com¬ 
mand, Eglin Field, Fla.), AAF Board Project No. 
4296C373.11, Oct. 29, 1945. 

268. Final Report on Training Method and Evaluation of the 
Acceleration Integrator Bomb Release, Training Research 
and Liaison Section, Williams Field, Chandler, Arizona, 
Project No. 7-2-45, Nov. 27, 1945. 




BIBLIOGRAPHY 


193 


ORS, 9th AF Hq. 

2G9. A Report on the Acceleration Integrator Bomb Release 
(AIBR) in the Ninth Air Force, Operational Research 
Section, 9th AF Headquarters, No. 107, Mar. 26, 1945. 

270. Flight Calibration of 7'oss Bombing Equipment in P-47 
Airplane, Research Section, 9th AF Headquarters, No. 
PWA-28-4A, Apr. 5, 1945, revised May 8, 1945. 

271. Operations of Toss Bombing Equipment in P-47-D Air¬ 
plane, Research Section, 9th AF Headquarters, No. 
PWA-28-4A(l), Apr. 5, 1945, revised May 8, 1945. 


272. Notes on the Inspection and Testing of Toss Bombing 
Equipment for Installation, Research Section, 9th Al' 
Headquarters, No. P\V.\-28-4A (2), Apr. 5, 1945, 
revised May 8, 1945. 

273. Maintenance Notes for AIBR {AN/ASG-10{XN) ), 
Re.search Section, 9th .\F Headquarters, No. P\VA-28- 
4.\(3), Apr. 5, 1945, revised May 8, 1945. 

274. Instructions for Installation: Bomb Director Mk 1 Mod 0 
(AN/ASG-IOXN) in P-47D Airplane, WF-0-1, 150, 
W16609, August 1945. 




OSRD APPOINTEES 


Division 4 


Chief 

Alexl\nder Ellett 


Technical Aides 

A. S. Clarke John S. Rinehart 

Sebastian ICvrrer E. R. Shaeffer 

Cathryn Pike A. G. Thomas 

R. M. Zabel 


M embers 

L. J. Briggs Harry Diamond 

W. D. CooLiDGE F. L. Hovde 

J. T. Tate 


Special Assistants 


M. G. Domsitz 
W. E. Elliott 
Wendell Gould 
W. S. Hinman, Jr. 


Joseph Ivaufman 
J. L. Thomas 

E. A. Turner 

F. C. Wood 


Consultants 


A. V. Astin 
R. A. Becker 
R. M. Bowie 
Cledo Brunetti 
J. W. DuMond 
Saul Dushman 
Wm. Fondiller 
T. B. Godfrey 
L. R. Hafstad 
J. E. Henderson 
R, D. Huntoon 
J. A. Jacobs 
R. B, Janes 
T. Lauritsen 


D. H. Loughridge 
W. B. McLean 
F. L. Mohler 
S. H. Neddermeyer 
PI. F. Olsen 
C. H. Page 
W. J. Shackelton 

F. B. SiLSBEE 

K. D. Smith 

G. W. Stewart 
J. F. Streib 

L. S. Taylor 
G. W. ViNAL 
W. L. Whitson 


R. M. Zabel 



CONTRACT NUMBERS, CONTRACTORS, AND SUBJECTS OF CONTRACTS 


Contract Number 

Name and Address of Contractor* 

Subject 

OEMsr-769 

University of Iowa 

Iowa City, Iowa 

Studies and experimental investigations in connec¬ 
tion with development work on special electronic 
devices and associated equipment. 

OEMsr-1227 

Bowen and Company, Inc. 

Bethesda, Maryland 

Furnish necessary machine shop and assembly 
facilities for the development of special electronic 
devices. 

OEMsr-1378 

Raymond Engineering Laboratory 

Berlin, Connecticut 

Studies and experimental investigations in connec¬ 
tion with development of special electronic de¬ 
vices. 

OEMsr-1417 

The Magnavox Company 

Fort Wayne, Indiana 

Design toss bombing equipment for production. 


* The National Bureau of Standards, which served as the central laboratories for Division 4, NDRC, did not operate under a contract but as a govern¬ 
ment agency under a direct transfer of funds from OSRD. 


195 








SERVICE PROJECT NUMBERS 


The projects listed below were transmitted to the Executive Secret¬ 
ary, NDRC, from the War or Navy Department through either the 
War Department Liaison Officer for NDRC or the Office of Research 
and Inventions (formerly the Coordinator of Research and Develop¬ 
ment), Navy Department. 


Service Project Number 


Subject 


Army Air Forces 
AC-62 


Development of toss bombing equipment. 


Navy 

NO-185 


Development of toss bombing ecpiipment. 


Ordnance Department 


Development of toss bombing equipment and techniques. 


OD-112 


196 








INDEX 


The subject indexes of all STR volume are combined in a master index printed in a separate volume. 
For access to the index volume consult the Army or Navy Agency listed on the reverse of the half-title page. 


Aiming procedures for lead-computing 
sight, 172-175 

Air resistance in bomb tossing, 127-129 
correction for air resistance, 129 
ground error, 128-129 
trajectory equations in air, 127-128 

Aircraft rockets, trajector}' drops, 139- 
141 

Altimeter for bomb directors 
air leakage, 48 
calibration, 47-48 

contact duration and continuity, 48 
electrical indicating, 73-75 
errors, 110-117 

for Mark 1 Model 0 bomb director, 
162-165 

for Mark 3 Model 0 bomb director, 
30-31 

installation, 50 
insulation resistance, 48 
laboratory testing, 47-48 
lag problem, 53-54 
position error, 48 

Attack angle variations, 120-127 

Automatic range wind correction, 135 

Banking limitation in gyro production 
problem, 43-44 

Bomb director, adjustment, 54-56 

Bomb director, altimeter unit 
see Altimeter for bomb directors 

Bomb director, equipment evaluation 
tests, 69-72 

Mark 1 Model 0; 70-72 
Mark 1 Model 1; 71-72 
no-wind mean point of impact 
(MPI), 69-72 

overall operation of Mark 1 bomb 
director, 69-70 

Bomb director, experimental produc¬ 
tion, 35-44 
computer, 38-39 
gyro, 39-44 
history, 35-38 

Bomb director, integration errors, 150- 
157 

accuracy determination methods, 
150-151 

accuracy of computer solution, 152 
analy.sis of discrepancies, 153-154 
comparison of experimental and the¬ 
oretical values, 156-157 
comparison of laboratory results with 
computer equation, 152 
conclusions, 157 


formula for instrumental pull-up 
time, 151 

laboratory testing, 151-152 
Bomb director, laboratory testing, 45- 
48 

altimeter unit, 47-48 
computer, 45-46 
control box, 48 
gyro, 46-47 

integration errors, 151-152 
objective, 45 

Bomb director, servicing, 59-61 
Bomb director, tactical evaluation 
tests, 62-69 

Eglin Field tests, 66-69 
low ceiling tests, 66 
mil error formula, 64-65 
Patuxent Naval Air Station tests, 
65, 67-69 

toss bombing compared to standard 
dive bombing, 65 
Bomb directors 

Mark 1 Model 0; 8-18, 70-90 
Mark 1 Model 1; 18, 30-34, 71-72 
Mark 1 Model 2; 34-35 
Mark 3 Model 0; 162-170 
Bomb tossing 

see also Toss bombing 
air resistance, 127-129 
basic equations, 6-8, 106-107 
equation solution, 94-100 
errors, 105-117, 176-181 
instrumental adjustments, 18, 117- 
127 

low altitude, 72 

mathematical analysis; see Mathe¬ 
matical analysis of bomb tossing 
mechanization of basic equation, 10- 
12 

release time, approximate solution, 
8-10 

theorjq 6-18 
trajectories, 14-18 

Bureau of Aeronautics bomb director 
experiments, 53-54 

Caging for gyros, 41-42 
Calibration tests 

rocket bombing, 52-53 
rocket tossing, 79 
toss bombing, 51-52 
Card potentiometer, 39-41 
Collision course, ground error, 132-133 
Collision cour.se in pre.sence of wind, 
130-132 


Collision course solution for lead-com¬ 
puting sight, 171-172 
Computers 
acceptance limits, 46 
commutator, 38-39 
equipment, 45-46 
laboratory testing, 45-46 
Mark 20 Model 1; 32-33 
Mark 20 Model 2; 34-35 
production problems, 38-39 
sealing, 38 

Dive angle indication for Mark 3 
Model 0 bomb director, 166-167 
Dive angle measurement, 108-109 
Dive-toss technique, 1-5 

comparison with ordinary di\'e bomb- 
i..g, 2-3 

models developed, 5 
performance summary, 3-5 
recommended release conditions, 3 
typical toss bombing attack, 1 
Dover Army Base rocket tossing field 
tests, 79 

Eglin Field tests on bomb directors, 
66-69 

Electrical indicating altimeter tests, 
73-75 

accuracy of altitude ratio, 74 
description, 73-74 
toss bombing runs, 74-75 
Equations for rocket tossing pull-up 
time, 141-150 

see also Bomb director, integration 
errors 

assumptions, 141-142 
change in attack angle during pull- 
up, 148-150 

equations of motion, 142-143 
lanyard fitting, 143-144 
notation, 142 

procedure for theoretical results, 141 
Equations for toss bombing, 6-18 
approximate solution for release time, 
8-10 

basic equations, 6-8 
mechanization of basic equations, 
10-12 

proper release time, 7-8 
spatial acceleration, 6-7 
trajectories, 14-18 

Equipment evaluation tests, bomb 
directors, 69-72 

Mark 1 Model 0 equipment, 70-72 



197 


198 


INDEX 


Mark 1 Model 1 equipment, 71-72 
no-wind mean point of impact 
(MPI), 69-72 

overall operation of Mark 1 bomb 
director, 69-70 

Equipment evaluation tests, rocket 
tossing, 82-90 

check on theoretical values, 90 
correction for tlecrease in MPI, 86 
effect of temperature controls on 
MPI, 87 

launching, 87-89 

MPI variation with dive angle, 83 
MPI variation with plane speed, 80, 
83 

MPI variation with pi'opellant tem¬ 
perature, 82, 84 

MPI variation with pull-up acceler¬ 
ation, 83-84 

MPI variation with slant range, 80- 
82 

overall performance, 84-86, 88 
salvo firing results, 91 
temperature compensation control 
calibration, 86 

Errors in bomb tossing, 105-117, 176- 
181 

altimeter errors, 110-116 
altitude errors, 117 
basic equation, 106-107 
incorrect measurement of dive angle, 
108-109 

range errors, 107-108, 110-116 
range limitations, 107-108 
systematic errors, analytical reduc¬ 
tion, 176-181 
types of error, 105-106 
Evaluation of toss technique, 62-93 
plane-to-plane tests, 91-93 
rocket tossing field tests, 76-90 
torpedo tossing field tests, 75-76 
toss bombing field tests, 62-75 

Flight test procedures, 51-54 
altimeter lag problem, 53-54 
calibration tests for rocket bombing, 
52-53 

calibration tests for toss bombing, 
51-52 

sight setting data, 52-53 
Ground error 

in collision course, 132-133 
in pursuit course, 134-135 
Gyro Mark 20 Model 1, (MX-329/ 
ASG-10), 31-32 
Gyro potentiometer, 102-104 
Gyros, laboratory testing, 46-47 
caging test, 46 
contact continuity, 46-47 


precession test, 46-47 
voltage, 47 

Gyros, production problems, 39-44 
banking limitation, 43-44 
caging, 41-42 

Kollsman altimeter (modified), 43-44 
i/' card potentiometer, 39-41 
shock mounting, 42-43 

Indicator lamp, (]\IX-339/ASG-10), 34 
Installation of toss bombing compo¬ 
nents, 49-51 
altimeter, 50-51 
computer, 49-50 
control boxes, 51 
gunsight, 51 
gyro, 50 

indicator lamp, 51 

Instrumental adjustment in bomb toss¬ 
ing, 117-127 

intervalometer chart, 117-118 
MPI adjustment, 118 
sight misalignment and attack angle 
variations, 120-127 
stick offset, 117-118 
torpedo tossing, 118-120 
Instrumental design theory, 102-105 
gyro potentiometer, 102-104 
stick-length offset, 105 
voltage variation with speed, 103-104 
Instrumental methods of wind correc¬ 
tion, 28, 136—137 
Instrumentation, 29-48 
assembly, 29-30 

bomb director Mark 1 Model 0; 35 
bomb director Mark 1 Model 1; 29- 

34 

bomb director Mark 1 Model 2; 34- 

35 

bomb directors, experimental pro¬ 
duction, 35-44 

laboratory testing of bomb directors, 
45-48 

production of bomb directors, 35-44 
Integrating circuit for Mark 3 Model 0 
bomb director, 167-168 
Integration errors, bomb director 
see Bomb director, integration errors 
Inyokern rocket tossing field tests, 78- 
79 

data evaluation method, 78-79 
tossing procedure, 78 

Kollsman altimeter (modified) 
prongs, 43-44 
shock mounting, 44 
w'hisker, 43 

Laboratory testing of bomb directors, 
45-48, 151-152 
altimeter unit, 47-48 


computer, 45-46 
control box, 48 
gyro, 46-47 

integration errors, 151-152 
objective, 45 
Lanyard firing, 143-144 
Lanyard launching, compensation for, 
23-24, 157-161 

comparison of experimental and the¬ 
oretical values, 161 
instrumentation and calibration, 
159-160 

method of compensation, 158-159 
Launching characteristics of rockets, 19 
Lead-computing sight, 170-176 
aiming procedures, 172-175 
basic differential equations, 170 
solution for collision course, 171-172 
wind correction, 175-176 

Maintenance of toss bombing equip¬ 
ment, 57-59 
ETO experience, 58-59 
field adjustments, 57 
naval air station experience, 57-58 
Mark 1 bomb directors 
advantages, 162 
effectiveness, 62-69 
firing delay time, 23-24 
instrumental adjustments, 18 
limitations, 162 
overall operation, 69-70 
proportionality constant, 6 
Quonset Naval Air Station tests, 72- 
75 

range limitations, 15-18 
Mark 1 bomb-rocket director, 21-23 
Mark 1 Model 0 bomb director 
as rocket director, 76-90 
equipment evaluation, 70-72 
instrumentation, 35 
mechanization of basic equation, 10- 
12 

simultaneous tossing of bombs and 
rockets, 73 

solution for release time, 8-10 
trajectories, 14-18 
Mark 1 Model 1 bomb director 
altimeter unit, 30-31 
assembly, 29 
computer, 32-33 
control box, 33-34 
equipment tests, 71-72 
gyro, 31-32 
indicator lamp, 34 
instrumental adjustments, 18 
mechanization of basic equation, 10- 
11, 14 

range limitations, 18 
switch box (transfer), 34 





INDEX 


199 


Mark 1 Model 2 bomb director, 34-35 
Mark 3 Model 0 bomb director, 162-170 
advantages over Mark 1 director, 170 
altimeter circuit, 162-165 
dive angle indication, 166-167 
integrating circuit, 167-168 
jjhotoelectric accelerometer, 165-166 
provision for firing rockets, 168-170 
wind correction, 167 
Mark 20 Model 1 computer, 32-33 
Mark 20 Model 2 computer, 34-35 
Mark 23 sighting head 
aiming procedures, 172-175 
wind correction, 175-176 
Mathematical analysis of bomb toss¬ 
ing, 94-138 

air resistance in bomb tossing, 127- 
129 

basic bomb tossing equation solution, 
94-100 

errors, 105-116 

instrumental adjustment in bomb 
tossing, 117-127 

instrumental design theory, 102-105 
particular pull-up acceleration, 100- 
102 

wind correction and target motion, 
130-138 

Mathematical theory of rocket tossing, 
139-161 

compensation for pro{)ellant temper¬ 
ature and lanyard launching, 
157-161 

, integration errors of bomb director, 
150-157 

pull-up time equations, 141-150 
trajectory drops, emijirical equation, 
139-141 

Mechanization of rocket tossing equa¬ 
tion, 21-23 

MPI (mean point of impact) equipment 
tests, 69-72 

MPI errors and remedies 
deflection errors, 55-56 
director, 55-56 
faulty bomb racks, 56 
sight setting, 56 
skidding, 56 

wind or target motion, 56 
MPI variation 
with dive angle, 83 
with plane speed, 80, 83 
with propellant temperature, 82-84 
with pull-up acceleration, 83-84 
with slant range, 80-82 

Operation of toss bombing equipment, 
54-57 

director, adjustment and use, 54-56 
iSIPI errors and remedies, 56-57 
optimum conditions, 54 
release time, 54 


Patuxent Naval Air Station, mainte¬ 
nance of toss bombing equip¬ 
ment, 57-58 

Patuxent Naval Air Station tests 
altimeter lag problem, 53-54 
equipment evaluation, 69-72 
rocket tossing, 76-77 
tactical evaluation, 65, 67-69 
Photoelectric accelerometer 

for ]\Iark 3 Model 0 bomb directoi-, 
165-166 

for wind compensation, 137-138 
Pilots’ evaluation tests, 63, 65 
Plane-to-plane tests, toss bombing, 91- 
93 

Production of bomb directois, 35-44 
computer, 38-39 
g\'ro, 39-44 
history, 35-38 

Propellant temperature and lanyard 
compensation, 23-24, 157-161 
comparison of expeiimental and the¬ 
oretical values, 161 
instrumentation and calibration,!59- 
160 

method of compensation, 158-159 
Pull-up acceleration, 100-102 
condition for kit, 101-102 
four types, 98, 100-101 
Pull-up time 

bombs and rockets compared, 21 
for rockets, 19-21 

Pull-up time equations, I'ocket tossing 
see Rocket tossing, pull-up time 
equations 
Pursuit course 
approach, 133-136 
ground error, 134-135 

(^uonset Naval Air Station tests, 72-77 
electrical indicating altimeter, 73-75 
low altitude bomb tossing, 72 
rocket tossing, 77 

simultaneous tossing of Ijombs and 
rockets, 73 

toss bombing combined with machine 
gun and rocket fire, 73 

Range errors in bomb tossing, 107-108, 
110-116 

Release conditions recommended for 
toss bombing, 3 

Release time for pursuit course ap¬ 
proach, 135-136 

Release time solution for bomb tossing, 
7-10 

Rocket firing, Mark 3 Model 0 bomb 
director, 168-170 
Rocket tossing, 18-25 
see also Toss bombing 
compensation for propellant temper¬ 
ature and lanyard, 23-24 


firing delay time, 23-24 
launching characteristics of rockets, 
19 

mechanization of equation, 21-23 
rocket trajectories, 18-19 
shift of impact point, 24-25 
Pocket tossing, field tests, 76-90 
I lover Army Base tests, 79 
(‘(luipment and procedure, 76-79 
(‘(iui{)ment evaluation tests, 79-90 
Inyokern tests, 78-79 
Patuxent tests, 76-77 
preliminary calibration tests, 79 
(^uonset tests, 77 

Pocket tossing, mathematical theory, 
139-161 

(•omp(‘nsation for propellant temper- 
atun; and lanyard launching, 
157-161 

integration errors of bomb director, 
150-157 

pull-up lime equations, 141-150 
t rajectory drops, empirical ('quations, 
139-141 

Pocket tossing, pull-up time equations, 

I 11-150 

sec also Bomb director, integration 
errors 

assumptions, 141-142 
change in attack angle during pull-up, 
148-150 

('([uations of motion, 142-143 
lanyard fitting, 143-144 
notation, 142 

j)rocedure for theoretical results, 141 
Pocket trajectories, 18-19 
Pockets, launching characteristics. It) 

Shock mounting for gyros, 42-43 
Sighting 

lead-computing sights, 170-176 
misalignment, 120-127 
sight settings for bomb and rocket 
tossing planes, 53 
wind correction method, 26-28 
Sp(n-ry artificial horizon gyroscope, 

“ 31-32, 39-44 

Standard Electric Time Co., electric 
timer, 59-61 
Stick offset, 117-118 
Stick-length offset, 105 

Tactical evaluation tests, boml) direc¬ 
tors, 62-69 

Eglin Field tests, 66-69 
low ceiling tests, 66 
mil error formula, 64-65 
Patuxent Naval Air Station tests, 
65, 67-69 

toss bombing compared to standard 
dive bombing, 65 




200 


INDEX 


Target motion, 130-138 
collision course, 130-132 
ground error in collision course, 132- 
133 

ground error in pursuit course, 134- 
135 

pursuit course approach, 133-134 
Test equipment for bomb director serv¬ 
icing, 59-61 

test unit Mark 16 Model 0; 59-61 
test unit Mark 17 Model 0; 61 
Tests at Patuxent Naval Air Station 
altimeter lag problem, 53-54 
equipment evaluation, 69-72 
rocket tossing, 76-77 
tactical evaluation, 65, 67-69 
Tests at Quonset Naval Air Station, 
72-75, 77 

electrical indicating altimeter, 73-75 
low altitude bomb tossing, 72 
rocket tossing, 77 

simultaneous tossing of bombs and 
rockets, 73 

toss bombing combined with ma¬ 
chine gun and rocket fire, 73 
Theodolite method for calibration in 
flight, 51-52, 79 
Theory of toss method 
bomb tossing, 6-18 
rocket tossing, 18-25 
torpedo tossing, 25-26 
wind correction, 26-28 
Torpedo tossing 
see also Toss bombing 
control box, 34 
field tests, 75-76 
theory, 25-26, 118-120 
Toss bombing 

see also Bomb tossing; Rocket toss¬ 
ing; Torpedo tossing 


Toss bombing components, installa¬ 
tion, 49-51 
altimeter, 50-51 
computer, 49-50 
camtrol boxes, 51 
gunsight, 51 
gyro, 50 

indicator lamp, 51 
Toss bombing equations, 6-18 

approximate solution for release time, 
8-10 

basic equations, 6-8 
mechanization of basic equations, 
10-12 

prop('r release time, 7-8 
spatial acceleration, 6-7 
trajectories, 14-18 

Toss bombing equipment, mainten¬ 
ance, 57-59 

Toss bombing equipment, operation, 
54-57 

director, adjustment and use, 54-56 
MPI errors and remedies, 56-57 
optimum conditions, 54 
release time, 54 

Toss bombing field tests, 62-75 
equipment evaluation tests, 69 
special tests, 72-75 
tactical evaluation tests, 62 
Toss method theory 
bomb tossing, 6-18 
rocket tossing, 18-25 
torpedo tossing, 25-26 
wind correction, 26-28 
Toss technique evaluation, 62-93 
plane-to-plane tests, 91-93 
rocket tossing field tests, 76-90 
torpedo tossing field tests, 75-76 
toss bombing field tests, 62-75 


Tossing equipment, improvements, 
162-181 

analytical reduction of systematic 
errors, 176-181 

lead-computing sight, 170-176 
Mark 1 bomb directors, 162 
Mark 3 Model 0 bomb director, 162- 
170 

Trajectories for bomb tossing 
air resistance, 127-128 
release conditions, 14-18 
Trajectory drops of aircraft rockets, 
empirical equations, 139-141 
formulation of equations fitting CIT 
data, 139-140 

unit conversion for theoretical work, 
140-141 

Wind compensation using photoelectric 
accelerometer, 137-138 
^^’ind correction, 26-28, 130-138 
automatic range wind correction, 135 
collision course in presence of wind, 
130-132 

for lead-computing sight, 175-176 
for Mark 3 Model 0 bomb director, 
167 

ground error in collision course, 132- 
133 

ground error in pursuit course, 134- 
135 

instrumental method, 28 
instrumentation, 136-137 
photoelectric accelerometer, 137-138 
pursuit course approach, 133-134 
release time for pursuit course ap¬ 
proach, 135-136 
sighting method, 26-28 









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